Theoretical and Mathematical Physics, ISSN 0040-5779, 12/2016, Volume 189, Issue 3, pp. 1681 - 1692

We describe a Bäcklund transformation, i.e., a differentially related pair of differential equations, in a coordinate manner appropriate for calculations and...

covariant derivative | gauge field | Theoretical, Mathematical and Computational Physics | total derivative | Bäcklund transformation | Yang–Mills field | partial differential equation | differential relation | constraint | Applications of Mathematics | curvature tensor | Physics | Yang-Mills field | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | Backlund transformation | PHYSICS, MATHEMATICAL | Differential equations

covariant derivative | gauge field | Theoretical, Mathematical and Computational Physics | total derivative | Bäcklund transformation | Yang–Mills field | partial differential equation | differential relation | constraint | Applications of Mathematics | curvature tensor | Physics | Yang-Mills field | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | Backlund transformation | PHYSICS, MATHEMATICAL | Differential equations

Journal Article

Ocean Engineering, ISSN 0029-8018, 03/2015, Volume 96, pp. 245 - 247

Nowadays, marine scientists are making use of the Kadomtsev-Petviashvili (KP)-category equations in their investigations from the Straits of Georgia and...

Shock waves | Fluids | Generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation | Symbolic computation | Bäcklund transformation | B-type | Kadomtsev-Petviashvili equation | Generalized (3+1)-dimensional variable-coefficient | ENGINEERING, CIVIL | SOLITONS | ENGINEERING, MARINE | ENGINEERING, OCEAN | INTERNAL WAVES | OCEANOGRAPHY | Generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation | Backlund transformation | ROGUE WAVES

Shock waves | Fluids | Generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation | Symbolic computation | Bäcklund transformation | B-type | Kadomtsev-Petviashvili equation | Generalized (3+1)-dimensional variable-coefficient | ENGINEERING, CIVIL | SOLITONS | ENGINEERING, MARINE | ENGINEERING, OCEAN | INTERNAL WAVES | OCEANOGRAPHY | Generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation | Backlund transformation | ROGUE WAVES

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 04/2018, Volume 92, Issue 2, pp. 709 - 720

Under investigation in this paper is the -dimensional B-type Kadomtsev-Petviashvili-Boussinesq (BKP-Boussinesq) equation, which can display the nonlinear...

Interaction phenomena | Rogue waves | Bäcklund transformation | Traveling waves | Kink solitary waves | Bell’s polynomial | BKP–Boussinesq equation | BREATHER WAVES | INTEGRABILITY | FLUID-DYNAMICS | BKP-Boussinesq equation | INFINITE CONSERVATION-LAWS | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | ENGINEERING, MECHANICAL | QUASI-PERIODIC WAVES | MECHANICS | Bell's polynomial | SOLITARY WAVES | (2+1)-DIMENSIONAL ITO EQUATION | Backlund transformation | RATIONAL CHARACTERISTICS | Water waves | Mineral industry | Mining industry | Nonlinear dynamics | Nonlinear equations | Boussinesq equations | Transformations (mathematics) | Nonlinear evolution equations | Polynomials | Identities | Solitary waves | Breathers

Interaction phenomena | Rogue waves | Bäcklund transformation | Traveling waves | Kink solitary waves | Bell’s polynomial | BKP–Boussinesq equation | BREATHER WAVES | INTEGRABILITY | FLUID-DYNAMICS | BKP-Boussinesq equation | INFINITE CONSERVATION-LAWS | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | ENGINEERING, MECHANICAL | QUASI-PERIODIC WAVES | MECHANICS | Bell's polynomial | SOLITARY WAVES | (2+1)-DIMENSIONAL ITO EQUATION | Backlund transformation | RATIONAL CHARACTERISTICS | Water waves | Mineral industry | Mining industry | Nonlinear dynamics | Nonlinear equations | Boussinesq equations | Transformations (mathematics) | Nonlinear evolution equations | Polynomials | Identities | Solitary waves | Breathers

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 03/2017, Volume 87, Issue 4, pp. 2529 - 2540

Under investigation in this paper is a -dimensional variable-coefficient generalized shallow water wave equation. Bilinear forms, Backlund transformation and...

(3 + 1)-dimensional variable-coefficient generalized shallow water wave equation | Soliton solutions | Bilinear forms | Periodic wave solutions | Bell polynomials | Bäcklund transformation | (3+1)-dimensional variable-coefficient generalized shallow water wave equation | SYSTEM | MECHANICS | BREATHERS | Backlund transformation | NONLINEAR SCHRODINGER-EQUATION | ENGINEERING, MECHANICAL | Fluid dynamics | Water waves | Amplitudes | Wave equations | Transformations | Polynomials | Coefficients | Shallow water | Solitary waves | Superposition (mathematics) | Combinatorial analysis

(3 + 1)-dimensional variable-coefficient generalized shallow water wave equation | Soliton solutions | Bilinear forms | Periodic wave solutions | Bell polynomials | Bäcklund transformation | (3+1)-dimensional variable-coefficient generalized shallow water wave equation | SYSTEM | MECHANICS | BREATHERS | Backlund transformation | NONLINEAR SCHRODINGER-EQUATION | ENGINEERING, MECHANICAL | Fluid dynamics | Water waves | Amplitudes | Wave equations | Transformations | Polynomials | Coefficients | Shallow water | Solitary waves | Superposition (mathematics) | Combinatorial analysis

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 10/2018, Volume 94, Issue 1, pp. 461 - 474

In this paper, the truncated Painleve expansion is employed to derive a Backlund transformation of a (2 + 1)-dimensional nonlinear system. This system can be...

Residual symmetry | Soliton–cnoidal wave solutions | (2 + 1)-dimensional sine-Gordon equation | CRE solvability | Bäcklund transformation | Lump-type solutions | WAVE INTERACTION SOLUTION | PAINLEV | (2+1)-dimensional sine-Gordon equation | Soliton-cnoidal wave solutions | ENGINEERING, MECHANICAL | ROBUST IDENTIFICATION | DIMENSIONS | MECHANICS | SCHIFF EQUATION | Backlund transformation | MODIFIED KDV EQUATION | NONLOCAL SYMMETRY | Cnoidal waves | Transformations | Nonlinear systems | Solitary waves | Symmetry

Residual symmetry | Soliton–cnoidal wave solutions | (2 + 1)-dimensional sine-Gordon equation | CRE solvability | Bäcklund transformation | Lump-type solutions | WAVE INTERACTION SOLUTION | PAINLEV | (2+1)-dimensional sine-Gordon equation | Soliton-cnoidal wave solutions | ENGINEERING, MECHANICAL | ROBUST IDENTIFICATION | DIMENSIONS | MECHANICS | SCHIFF EQUATION | Backlund transformation | MODIFIED KDV EQUATION | NONLOCAL SYMMETRY | Cnoidal waves | Transformations | Nonlinear systems | Solitary waves | Symmetry

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 12/2015, Volume 50, pp. 37 - 42

We directly construct a bilinear Bäcklund transformation (BT) of a (2+1)-dimensional Korteweg–de Vries-like model. The construction is based on a so-called...

Quadrilinear representation | Bilinear Bäcklund transformation | Multisoliton solutions | MATHEMATICS, APPLIED | BELL POLYNOMIALS | INTEGRABILITY | REPRESENTATION | RESONANT SOLUTIONS | NONLINEAR SCHRODINGER-EQUATION | SOLITON-SOLUTIONS | Bilinear Backlund transformation | COMBINATORICS | OPERATORS | OPTICAL-FIBER COMMUNICATIONS

Quadrilinear representation | Bilinear Bäcklund transformation | Multisoliton solutions | MATHEMATICS, APPLIED | BELL POLYNOMIALS | INTEGRABILITY | REPRESENTATION | RESONANT SOLUTIONS | NONLINEAR SCHRODINGER-EQUATION | SOLITON-SOLUTIONS | Bilinear Backlund transformation | COMBINATORICS | OPERATORS | OPTICAL-FIBER COMMUNICATIONS

Journal Article

Physics Letters A, ISSN 0375-9601, 02/2018, Volume 382, Issue 5, pp. 253 - 258

The N=2a=−2 supersymmetric KdV equation is studied. A Darboux transformation and the corresponding Bäcklund transformation are constructed for this equation....

Supersymmetric integrable system | Nonlinear superposition formula | Bäcklund transformation | Darboux transformation | Discrete integrable system | SOLITON-SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | SUPER-KDV | ALGEBRA | EXTENSION | Backlund transformation | BILINEAR FORM

Supersymmetric integrable system | Nonlinear superposition formula | Bäcklund transformation | Darboux transformation | Discrete integrable system | SOLITON-SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | SUPER-KDV | ALGEBRA | EXTENSION | Backlund transformation | BILINEAR FORM

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 11/2019, Volume 42, Issue 16, pp. 5154 - 5158

In this paper, we study the Bäcklund transformations for the adjoint curve in the Euclidean 3‐space. Firstly, it is obtained some essential equations of the...

Adjoint curve | Bäcklund transformations | Frenet frame | MATHEMATICS, APPLIED | Backlund transformations | Euclidean geometry | Transformations

Adjoint curve | Bäcklund transformations | Frenet frame | MATHEMATICS, APPLIED | Backlund transformations | Euclidean geometry | Transformations

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 2015, Volume 80, Issue 1-2, pp. 1 - 7

A (3+1)-dimensional B-type Kadomtsev-Petviashvili equation, which can be applied to describe the propagation of non-linear waves in fluid dynamics, is under...

Hirota method | Bäcklund transformations | Soliton solutions | (3 + 1)-Dimensional B-type Kadomtsev–Petviashvili equation | Bell polynomials | WAVES | MECHANICS | (3+1)-Dimensional B-type Kadomtsev-Petviashvili equation | DE-VRIES EQUATION | LATTICE | ENGINEERING, MECHANICAL | Backlund transformations | Fluid dynamics | Dynamic tests | Wave propagation | Computational fluid dynamics | Transformations | Polynomials | Solitary waves | Combinatorial analysis

Hirota method | Bäcklund transformations | Soliton solutions | (3 + 1)-Dimensional B-type Kadomtsev–Petviashvili equation | Bell polynomials | WAVES | MECHANICS | (3+1)-Dimensional B-type Kadomtsev-Petviashvili equation | DE-VRIES EQUATION | LATTICE | ENGINEERING, MECHANICAL | Backlund transformations | Fluid dynamics | Dynamic tests | Wave propagation | Computational fluid dynamics | Transformations | Polynomials | Solitary waves | Combinatorial analysis

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 10/2016, Volume 60, pp. 96 - 100

Under investigation in this paper is a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation, which describes the...

[formula omitted]-dimensional generalized variable-coefficient B-type Kadomtsev–Petviashvili equation | Fluids | Soliton solutions | Bell polynomials | Bäcklund transformation | (3+1)-dimensional generalized variable-coefficient B-type Kadomtsev-Petviashvili equation | MATHEMATICS, APPLIED | BREATHERS | Kadomtsev-Petviashvili equation | Backlund transformation | (3+1)-dimensional generalized variable-coefficient B-type | ROGUE WAVES | Fluid dynamics

[formula omitted]-dimensional generalized variable-coefficient B-type Kadomtsev–Petviashvili equation | Fluids | Soliton solutions | Bell polynomials | Bäcklund transformation | (3+1)-dimensional generalized variable-coefficient B-type Kadomtsev-Petviashvili equation | MATHEMATICS, APPLIED | BREATHERS | Kadomtsev-Petviashvili equation | Backlund transformation | (3+1)-dimensional generalized variable-coefficient B-type | ROGUE WAVES | Fluid dynamics

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 02/2013, Volume 219, Issue 11, pp. 5837 - 5848

A new integrable hierarchy of evolution equations is obtained by making use of a Lie algebra and Tu–Ma scheme, from which a new generalized Broer–Kaup (gBK)...

Bell polynomials | Bäcklund transformation | Integrable hierarchy | MATHEMATICS, APPLIED | Backlund transformation | CLASSICAL BOUSSINESQ SYSTEM | HAMILTONIAN-STRUCTURE

Bell polynomials | Bäcklund transformation | Integrable hierarchy | MATHEMATICS, APPLIED | Backlund transformation | CLASSICAL BOUSSINESQ SYSTEM | HAMILTONIAN-STRUCTURE

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 03/2019, Volume 89, pp. 103 - 110

In this paper, the truncated Painlevé expansion is employed to derive the Bäcklund transformation and the nth Bäcklund transformation of the modified...

Soliton–cnoidal wave solutions | Modified Kadomtsev–Petviashvili equation | Rational solutions | Bäcklund transformation | MATHEMATICS, APPLIED | Modified Kadomtsev-Petviashvili equation | EXPLICIT SOLUTIONS | CRE SOLVABILITY | LUMP-KINK SOLUTIONS | Backlund transformation | Soliton-cnoidal wave solutions | NONLOCAL SYMMETRY

Soliton–cnoidal wave solutions | Modified Kadomtsev–Petviashvili equation | Rational solutions | Bäcklund transformation | MATHEMATICS, APPLIED | Modified Kadomtsev-Petviashvili equation | EXPLICIT SOLUTIONS | CRE SOLVABILITY | LUMP-KINK SOLUTIONS | Backlund transformation | Soliton-cnoidal wave solutions | NONLOCAL SYMMETRY

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 04/2019, Volume 69, pp. 78 - 97

•A new extended Painlevé hierarchy.•Bäcklund and auto-Bäcklund transformations, nesting, and other properties.•Importance of underlying structure of equations....

Bäcklund transformations | Extended Painleváe hierarchy | ORDER DIFFERENTIAL-EQUATIONS | INTEGRALS | MATHEMATICS, APPLIED | 1ST | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYMMETRIES | 3RD-ORDER | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | Extended Painlevae hierarchy | Backlund transformations

Bäcklund transformations | Extended Painleváe hierarchy | ORDER DIFFERENTIAL-EQUATIONS | INTEGRALS | MATHEMATICS, APPLIED | 1ST | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYMMETRIES | 3RD-ORDER | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | Extended Painlevae hierarchy | Backlund transformations

Journal Article

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 01/2019, Volume 118, pp. 337 - 346

•Under investigation is a higher-order nonlinear Schrodinger system for the simultaneous propagation of two ultrashort optical pulses in an optical fiber.•With...

Conservation laws | Higher-order nonlinear Schrödinger system | Nondegenerate dark–dark soliton | Binary Darboux transformations | INTEGRABILITY | Higher-order nonlinear Schrodinger system | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | PHYSICS, MATHEMATICAL | COLLISIONS | DARK SOLITON | BACKLUND TRANSFORMATION | PAINLEVE ANALYSIS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | OPTICAL-FIBER | BREATHERS | Nondegenerate dark-dark soliton | BRIGHT

Conservation laws | Higher-order nonlinear Schrödinger system | Nondegenerate dark–dark soliton | Binary Darboux transformations | INTEGRABILITY | Higher-order nonlinear Schrodinger system | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | PHYSICS, MATHEMATICAL | COLLISIONS | DARK SOLITON | BACKLUND TRANSFORMATION | PAINLEVE ANALYSIS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | OPTICAL-FIBER | BREATHERS | Nondegenerate dark-dark soliton | BRIGHT

Journal Article

Physics Letters A, ISSN 0375-9601, 07/2018, Volume 382, Issue 29, pp. 1908 - 1915

We derive auto-Bäcklund transformations, analogous to those of the matrix second Painlevé equation, for a matrix partial differential equation. We also then...

Matrix partial differential equations | Auto-Bäcklund transformations | BURGERS | UNIFIED APPROACH | PHYSICS, MULTIDISCIPLINARY | TRUNCATION | NONISOSPECTRAL SCATTERING PROBLEMS | EXTENSION | Auto-Backlund transformations | EVOLUTION-EQUATIONS | PAINLEVE PROPERTY | DARBOUX TRANSFORMATIONS

Matrix partial differential equations | Auto-Bäcklund transformations | BURGERS | UNIFIED APPROACH | PHYSICS, MULTIDISCIPLINARY | TRUNCATION | NONISOSPECTRAL SCATTERING PROBLEMS | EXTENSION | Auto-Backlund transformations | EVOLUTION-EQUATIONS | PAINLEVE PROPERTY | DARBOUX TRANSFORMATIONS

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 8/2017, Volume 89, Issue 3, pp. 2233 - 2240

In this paper, a $$(3+1)$$ ( 3 + 1 ) -dimensional nonlinear evolution equation is cast into Hirota bilinear form with a dependent variable transformation. A...

Engineering | Vibration, Dynamical Systems, Control | Classical Mechanics | Bäcklund transformation | 35Q55 | Automotive Engineering | Nonresonant multiple wave solutions | Mechanical Engineering | 37K40 | Symbolic computation | 35Q51 | Lump solution | RATIONAL SOLUTIONS | MECHANICS | SOLITONS | SCHRODINGER-EQUATION | MEDIA | HIROTA BILINEAR EQUATION | Backlund transformation | ENGINEERING, MECHANICAL | Nonlinear evolution equations | Exponential functions | Wave propagation | Transformations (mathematics) | Dependent variables

Engineering | Vibration, Dynamical Systems, Control | Classical Mechanics | Bäcklund transformation | 35Q55 | Automotive Engineering | Nonresonant multiple wave solutions | Mechanical Engineering | 37K40 | Symbolic computation | 35Q51 | Lump solution | RATIONAL SOLUTIONS | MECHANICS | SOLITONS | SCHRODINGER-EQUATION | MEDIA | HIROTA BILINEAR EQUATION | Backlund transformation | ENGINEERING, MECHANICAL | Nonlinear evolution equations | Exponential functions | Wave propagation | Transformations (mathematics) | Dependent variables

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 03/2018, Volume 126, pp. 148 - 158

In classical mechanics well-known cryptographic algorithms and protocols can be very useful for construction of canonical transformations preserving form of...

Separation of variables | Integrable systems | Arithmetic of divisors | Backlund transformations | MATHEMATICS | SYSTEMS | SEPARATION | PHYSICS, MATHEMATICAL | Algorithms

Separation of variables | Integrable systems | Arithmetic of divisors | Backlund transformations | MATHEMATICS | SYSTEMS | SEPARATION | PHYSICS, MATHEMATICAL | Algorithms

Journal Article

Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 10/2016, Volume 31, pp. 388 - 408

Under investigation in this paper is a generalized (2+1)-dimensional Boussinesq equation, which can be used to describe the water wave interaction. By using...

The (2+1)-dimensional Boussinesq equation | Bell’s polynomials | Soliton solution | Periodic wave solution | Infinite conservation laws | Bäcklund transformation | Bell's polynomials | POLYNOMIALS | MATHEMATICS, APPLIED | CAMASSA-HOLM EQUATION | Backlund transformation | RATIONAL CHARACTERISTICS | Environmental law

The (2+1)-dimensional Boussinesq equation | Bell’s polynomials | Soliton solution | Periodic wave solution | Infinite conservation laws | Bäcklund transformation | Bell's polynomials | POLYNOMIALS | MATHEMATICS, APPLIED | CAMASSA-HOLM EQUATION | Backlund transformation | RATIONAL CHARACTERISTICS | Environmental law

Journal Article

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, ISSN 0002-9947, 02/2020, Volume 373, Issue 2, pp. 1181 - 1210

Using Elie Cartan's method of equivalence, we prove an upper bound for the generality of generic rank-1 Backlund transformations relating two hyperbolic...

MATHEMATICS | exterior differential systems | Cartan's method of equivalence | hyperbolic Monge-Ampere systems | Backlund transformations

MATHEMATICS | exterior differential systems | Cartan's method of equivalence | hyperbolic Monge-Ampere systems | Backlund transformations

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 03/2017, Volume 44, pp. 360 - 372

•Under investigation in this paper is a (2+1)-dimensional Broer-Kaup-Kupershmidt system for the nonlinear and dispersive long gravity waves on two horizontal...

Soliton solutions | (2+1)-Dimensional broer-Kaup-Kupershmidt system | Lax pair | Bell polynomials | Shallow water of uniform depth | Bäcklund transformation | MATHEMATICS, APPLIED | BOUSSINESQ EQUATION | FORM | PHYSICS, FLUIDS & PLASMAS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | ROGUE WAVES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | RESONANCE | Backlund transformation | CONSERVATION-LAWS | KORTEWEG-DEVRIES | Fluid dynamics

Soliton solutions | (2+1)-Dimensional broer-Kaup-Kupershmidt system | Lax pair | Bell polynomials | Shallow water of uniform depth | Bäcklund transformation | MATHEMATICS, APPLIED | BOUSSINESQ EQUATION | FORM | PHYSICS, FLUIDS & PLASMAS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | ROGUE WAVES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | RESONANCE | Backlund transformation | CONSERVATION-LAWS | KORTEWEG-DEVRIES | Fluid dynamics

Journal Article