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

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

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

2002, Cambridge texts in applied mathematics., ISBN 052181331X, xvii, 413

This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors also...

Darboux transformations | Bäcklund transformations | Solitons

Darboux transformations | Bäcklund transformations | Solitons

Book

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

1977, Interdisciplinary mathematics ; v. 15., ISBN 9780915692200, v.

Book

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

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

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

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

Nonlinear Dynamics, ISSN 0924-090X, 4/2014, Volume 76, Issue 1, pp. 161 - 168

In this paper, the (2+1)-dimensional Sawada–Kotera model is studied with the Hirota bilinear method, gauge transformation and symbolic computation. Based on an...

Engineering | Vibration, Dynamical Systems, Control | Bilinear Bäcklund transformation | Gauge transformation | Multisoliton solutions | Mechanics | (2+1)-Dimensional Sawada–Kotera model | Automotive Engineering | Mechanical Engineering | Symbolic computation | SYSTEM | FLUID-DYNAMICS | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | ENGINEERING, MECHANICAL | WAVE | MECHANICS | SOLITON-SOLUTIONS | Bilinear Backlund transformation | (2+1)-Dimensional Sawada-Kotera model | OPTICAL-FIBER COMMUNICATIONS | Models | Traffic regulations | Perturbation methods | Solitary waves | Transformations

Engineering | Vibration, Dynamical Systems, Control | Bilinear Bäcklund transformation | Gauge transformation | Multisoliton solutions | Mechanics | (2+1)-Dimensional Sawada–Kotera model | Automotive Engineering | Mechanical Engineering | Symbolic computation | SYSTEM | FLUID-DYNAMICS | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | ENGINEERING, MECHANICAL | WAVE | MECHANICS | SOLITON-SOLUTIONS | Bilinear Backlund transformation | (2+1)-Dimensional Sawada-Kotera model | OPTICAL-FIBER COMMUNICATIONS | Models | Traffic regulations | Perturbation methods | Solitary waves | Transformations

Journal Article

1982, ISBN 0125928505, Volume 161., xiii, 334

Book

1979, SIAM studies in applied mathematics ; 1., ISBN 0898711517, Volume 1., x, 124

Book

Applied Mathematical Modelling, ISSN 0307-904X, 06/2015, Volume 39, Issue 12, pp. 3221 - 3226

With symbolic computation, Bell-polynomial scheme and bilinear method are applied to a two-dimensional Korteweg–de Vries (KdV) model, which is firstly proposed...

Bilinear method | Bell-polynomial-typed Bäcklund transformation | Symbolic computation | Bell polynomials | Two-dimensional Korteweg–de Vries model | Two-dimensional Korteweg-de Vries model | BOUSSINESQ EQUATION | Bell-polynomial-typed Backlund transformation | NONLINEAR SCHRODINGER-EQUATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | ONE TAU-FUNCTION | CONSTRUCTION | WAVE-EQUATION | KDV EQUATION | COMBINATORICS | OPTICAL-FIBER COMMUNICATIONS

Bilinear method | Bell-polynomial-typed Bäcklund transformation | Symbolic computation | Bell polynomials | Two-dimensional Korteweg–de Vries model | Two-dimensional Korteweg-de Vries model | BOUSSINESQ EQUATION | Bell-polynomial-typed Backlund transformation | NONLINEAR SCHRODINGER-EQUATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | ONE TAU-FUNCTION | CONSTRUCTION | WAVE-EQUATION | KDV EQUATION | COMBINATORICS | OPTICAL-FIBER COMMUNICATIONS

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 11/2019, Volume 361, pp. 389 - 397

We first establish a one-fold Darboux–Bäcklund transformation for the integrable differential-difference equation which is presented in Ref. [6] by means of a...

Darboux–Bäcklund transformation | Integrable different-difference equation | Lax pair | Gauge transformation | Exact solution | IDENTITY | MATHEMATICS, APPLIED | Darboux-Backlund transformation | HIERARCHY

Darboux–Bäcklund transformation | Integrable different-difference equation | Lax pair | Gauge transformation | Exact solution | IDENTITY | MATHEMATICS, APPLIED | Darboux-Backlund transformation | HIERARCHY

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 09/2015, Volume 70, Issue 5, pp. 765 - 775

The multiple Exp-function method is used to construct multiple wave solutions to the (3+1)-dimensional generalized BKP equation. The resulting solutions...

Generalized BKP equation | Auto-Bäcklund transformation | Hyperbolic and trigonometric function solutions | Multiple wave solutions | MATHEMATICS, APPLIED | TOPOLOGICAL SOLITONS | HIROTA BILINEAR EQUATIONS | 1-SOLITON SOLUTION | PERTURBATION | Auto-Backlund transformation | EXP-FUNCTION METHOD | JIMBO-MIWA EQUATION | LINEAR-SUBSPACES | WRONSKIAN SOLUTIONS | POWER-LAW NONLINEARITY

Generalized BKP equation | Auto-Bäcklund transformation | Hyperbolic and trigonometric function solutions | Multiple wave solutions | MATHEMATICS, APPLIED | TOPOLOGICAL SOLITONS | HIROTA BILINEAR EQUATIONS | 1-SOLITON SOLUTION | PERTURBATION | Auto-Backlund transformation | EXP-FUNCTION METHOD | JIMBO-MIWA EQUATION | LINEAR-SUBSPACES | WRONSKIAN SOLUTIONS | POWER-LAW NONLINEARITY

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 09/2018, Volume 83, pp. 33 - 39

Based on the residual symmetry theorem, the residual symmetry is obtained for the (2+1)-dimensional generalized Broer–Kaup (GBK) equations. The multiple...

Residual symmetry | Interaction solution | [formula omitted]th Bäcklund transformation | Consistent tanh expansion method | (2+1)-dimensional generalized Broer–Kaup equations | nth Bäcklund transformation | PAINLEVE ANALYSIS | MATHEMATICS, APPLIED | SOLVABILITY | Broer Kaup equations | (2+1)-dimensional generalized | nth Backlund transformation

Residual symmetry | Interaction solution | [formula omitted]th Bäcklund transformation | Consistent tanh expansion method | (2+1)-dimensional generalized Broer–Kaup equations | nth Bäcklund transformation | PAINLEVE ANALYSIS | MATHEMATICS, APPLIED | SOLVABILITY | Broer Kaup equations | (2+1)-dimensional generalized | nth Backlund transformation

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 2/2016, Volume 83, Issue 3, pp. 1199 - 1215

A generalized (3+1)-dimensional nonlinear wave is investigated, which describes many nonlinear phenomena in liquid containing gas bubbles. In this paper, a...

Engineering | Vibration, Dynamical Systems, Control | A generalized (3+1)-dimensional nonlinear wave equation | Soliton solution | Infinite conservation laws | Bäcklund transformation | Mechanics | Bell’s polynomials | Automotive Engineering | Mechanical Engineering | Periodic wave solution | SYSTEM | 1-SOLITON SOLUTION | MODEL | ENGINEERING, MECHANICAL | MECHANICS | EVOLUTION | SOLITONS | BILINEAR EQUATIONS | KDV EQUATION | Backlund transformation | RATIONAL CHARACTERISTICS | Bell's polynomials | Environmental law | Conservation laws | Bubbles | Nonlinear phenomena | Transformations (mathematics) | Integral equations | Wave equations | Polynomials | Fluxes | Solitary waves

Engineering | Vibration, Dynamical Systems, Control | A generalized (3+1)-dimensional nonlinear wave equation | Soliton solution | Infinite conservation laws | Bäcklund transformation | Mechanics | Bell’s polynomials | Automotive Engineering | Mechanical Engineering | Periodic wave solution | SYSTEM | 1-SOLITON SOLUTION | MODEL | ENGINEERING, MECHANICAL | MECHANICS | EVOLUTION | SOLITONS | BILINEAR EQUATIONS | KDV EQUATION | Backlund transformation | RATIONAL CHARACTERISTICS | Bell's polynomials | Environmental law | Conservation laws | Bubbles | Nonlinear phenomena | Transformations (mathematics) | Integral equations | Wave equations | Polynomials | Fluxes | Solitary waves

Journal Article

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