1.
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Abundant soliton solutions for the Kundu–Eckhaus equation via tan(ϕ(ξ))-expansion method

Optik - International Journal for Light and Electron Optics, ISSN 0030-4026, 07/2016, Volume 127, Issue 14, pp. 5543 - 5551

In this paper, the improved tanΦ(ξ)/2-expansion method is proposed to seek more general exact solutions of the Kundu–Eckhaus equation. Being concise and...

Periodic and rational solutions | Improved [formula omitted]-expansion method | Kink | Kundu–Eckhaus equation | Solitons | Kundu-Eckhaus equation | Improved tan (Φ(ξ))-expansion method | Improved tan (Phi(xi)/2)-expansion method | BISWAS-MILOVIC EQUATION | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | OPTICAL SOLITONS | BACKLUND TRANSFORMATION | TRAVELING-WAVE SOLUTIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | COEFFICIENTS | SYSTEMS | OPTICS | Methods | Differential equations | Partial differential equations | Searching | Mathematical analysis | Nonlinear differential equations | Exact solutions | Hyperbolic functions | Trigonometric functions

Periodic and rational solutions | Improved [formula omitted]-expansion method | Kink | Kundu–Eckhaus equation | Solitons | Kundu-Eckhaus equation | Improved tan (Φ(ξ))-expansion method | Improved tan (Phi(xi)/2)-expansion method | BISWAS-MILOVIC EQUATION | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | OPTICAL SOLITONS | BACKLUND TRANSFORMATION | TRAVELING-WAVE SOLUTIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | COEFFICIENTS | SYSTEMS | OPTICS | Methods | Differential equations | Partial differential equations | Searching | Mathematical analysis | Nonlinear differential equations | Exact solutions | Hyperbolic functions | Trigonometric functions

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 11/2018, Volume 85, pp. 77 - 81

Many mixed lump–soliton solutions for the (3+1)-dimensional integrable equation are obtained by using the Hirota bilinear method. These mixed lump–soliton...

Mixed lump–soliton solutions | The [formula omitted]-dimensional integrable equation | Hirota bilinear method | The (3+1)-dimensional integrable equation | TRANSFORMATION | MATHEMATICS, APPLIED | EXPLICIT SOLUTIONS | DIFFERENCE | Mixed lump-soliton solutions | WAVE SOLUTIONS

Mixed lump–soliton solutions | The [formula omitted]-dimensional integrable equation | Hirota bilinear method | The (3+1)-dimensional integrable equation | TRANSFORMATION | MATHEMATICS, APPLIED | EXPLICIT SOLUTIONS | DIFFERENCE | Mixed lump-soliton solutions | WAVE SOLUTIONS

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 01/2018, Volume 75, Issue 1, pp. 1 - 6

In this work, we construct multi-soliton solutions of the (2+1)-dimensional breaking soliton equation with variable coefficients by using the generalized...

The generalized unified method | The [formula omitted]-dimensional breaking soliton equation | Multi-wave solutions | Variable coefficients | The (2+1)-dimensional breaking soliton equation | MATHEMATICS, APPLIED | STABILITY

The generalized unified method | The [formula omitted]-dimensional breaking soliton equation | Multi-wave solutions | Variable coefficients | The (2+1)-dimensional breaking soliton equation | MATHEMATICS, APPLIED | STABILITY

Journal Article

4.
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Bright and dark soliton solutions for a K ( m , n ) equation with t-dependent coefficients

Physics Letters A, ISSN 0375-9601, 2009, Volume 373, Issue 25, pp. 2162 - 2165

The propagation of soliton pulses in an inhomogeneous media that is described by a K ( m , n ) equation with t-dependent coefficients is studied. By using a...

Bright and dark soliton solution | sech and tanh ansatzes | Variable-coefficient [formula omitted] equation | Variable-coefficient K (m, n) equation | GENERALIZED EVOLUTION | PHYSICS, MULTIDISCIPLINARY | Variable-coefficient K(m, n) equation sech and tanh ansatzes | 1-SOLITON SOLUTION | COMPACTONS | PATTERNS | KDV | NONLINEAR DISPERSIVE K(M | Wave propagation | Radiation | Universities and colleges

Bright and dark soliton solution | sech and tanh ansatzes | Variable-coefficient [formula omitted] equation | Variable-coefficient K (m, n) equation | GENERALIZED EVOLUTION | PHYSICS, MULTIDISCIPLINARY | Variable-coefficient K(m, n) equation sech and tanh ansatzes | 1-SOLITON SOLUTION | COMPACTONS | PATTERNS | KDV | NONLINEAR DISPERSIVE K(M | Wave propagation | Radiation | Universities and colleges

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 06/2018, Volume 75, Issue 11, pp. 3939 - 3945

In this letter, the linear superposition principle is used to discuss the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation with bilinear derivatives. As...

Resonant soliton and complexiton solutions | [formula omitted]-dimensional Boiti–Leon–Manna–Pempinelli equation | Linear superposition principle | (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation | RATIONAL SOLUTIONS | MATHEMATICS, APPLIED | HIROTA BILINEAR EQUATIONS | WAVE SOLUTIONS | ROGUE WAVE | (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

Resonant soliton and complexiton solutions | [formula omitted]-dimensional Boiti–Leon–Manna–Pempinelli equation | Linear superposition principle | (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation | RATIONAL SOLUTIONS | MATHEMATICS, APPLIED | HIROTA BILINEAR EQUATIONS | WAVE SOLUTIONS | ROGUE WAVE | (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 01/2018, Volume 75, pp. 114 - 120

In this paper, a discrete Hirota equation is analytically investigated. The N-fold Darboux transformation (DT) is constructed based on the Lax pair for the...

[formula omitted]-fold Darboux transformation | A discrete Hirota equation | Explicit discrete solutions | N-fold Darboux transformation | MATHEMATICS, APPLIED | NONLINEAR SCHRODINGER-EQUATION | LATTICE

[formula omitted]-fold Darboux transformation | A discrete Hirota equation | Explicit discrete solutions | N-fold Darboux transformation | MATHEMATICS, APPLIED | NONLINEAR SCHRODINGER-EQUATION | LATTICE

Journal Article

Physics Letters A, ISSN 0375-9601, 08/2017, Volume 381, Issue 30, pp. 2380 - 2385

In this paper, we succeed to bilinearize the PT-invariant nonlocal nonlinear Schrödinger (NNLS) equation through a nonstandard procedure and present more...

Bright soliton solution | [formula omitted]-symmetry | Nonstandard bilinearization | Nonlocal nonlinear Schrödinger equation | PT-symmetry | Nonlocal nonlinear Schrodinger equation | 2T-symmetry | PHYSICS, MULTIDISCIPLINARY

Bright soliton solution | [formula omitted]-symmetry | Nonstandard bilinearization | Nonlocal nonlinear Schrödinger equation | PT-symmetry | Nonlocal nonlinear Schrodinger equation | 2T-symmetry | PHYSICS, MULTIDISCIPLINARY

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 08/2018, Volume 82, pp. 126 - 131

In this paper, we investigate the (2+1)-dimensional stochastic Broer–Kaup equations for the shallow water wave in a fluid or electrostatic wave in a plasma....

[formula omitted]-dimensional stochastic Broer–Kaup equation | Fluid or plasma | Soliton solutions | White noise functional approach | (2+1)-dimensional stochastic Broer–Kaup equation | MATHEMATICS, APPLIED | (2+1)-dimensional stochastic | Broer-Kaup equation | NONLINEAR SCHRODINGER-EQUATION

[formula omitted]-dimensional stochastic Broer–Kaup equation | Fluid or plasma | Soliton solutions | White noise functional approach | (2+1)-dimensional stochastic Broer–Kaup equation | MATHEMATICS, APPLIED | (2+1)-dimensional stochastic | Broer-Kaup equation | NONLINEAR SCHRODINGER-EQUATION

Journal Article

Physics Letters A, ISSN 0375-9601, 2008, Volume 372, Issue 9, pp. 1422 - 1428

A new ( 2 + 1 )-dimensional soliton equation and its spectral problems are presented. The Darboux transformation with multi-parameters for the spectral...

Soliton solution | ( [formula omitted])-dimensional soliton equation | Darboux transformation | (2 + 1)-dimensional soliton equation | MULTISOLITON SOLUTIONS | EXPLICIT SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | soliton solution | CONSTRAINTS | CLASSICAL BOUSSINESQ SYSTEM | (2+1)-dimensional soliton equation | Computer science

Soliton solution | ( [formula omitted])-dimensional soliton equation | Darboux transformation | (2 + 1)-dimensional soliton equation | MULTISOLITON SOLUTIONS | EXPLICIT SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | soliton solution | CONSTRAINTS | CLASSICAL BOUSSINESQ SYSTEM | (2+1)-dimensional soliton equation | Computer science

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 08/2017, Volume 74, Issue 3, pp. 504 - 512

A (2+1)-dimensional Vakhnenko equation is investigated, which describes high-frequent wave propagations in relaxing medium. The N-loop soliton solutions for...

Improved Hirota method | [formula omitted]-dimensional Vakhnenko equation | N-loop soliton solution | Soliton interactions | (2+1)-dimensional Vakhnenko equation | MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | EVOLUTION EQUATION | SHORT-PULSE EQUATION | MULTISOLITON | Wave propagation

Improved Hirota method | [formula omitted]-dimensional Vakhnenko equation | N-loop soliton solution | Soliton interactions | (2+1)-dimensional Vakhnenko equation | MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | EVOLUTION EQUATION | SHORT-PULSE EQUATION | MULTISOLITON | Wave propagation

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 09/2016, Volume 59, pp. 115 - 121

In this paper, by employing the Hirota’s bilinear method, we construct the N-soliton solution for an integrable nonlocal discrete focusing nonlinear...

Hirota’s bilinear method | Discrete nonlocal Schrödinger equation | [formula omitted]-soliton solution | Hirota's bilinear method | N-soliton solution

Hirota’s bilinear method | Discrete nonlocal Schrödinger equation | [formula omitted]-soliton solution | Hirota's bilinear method | N-soliton solution

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2018, Volume 460, Issue 1, pp. 476 - 486

In this paper, we investigate the (2+1)-dimensional Konopelchenko–Dubrovsky equations. Via the Sato theory and Hirota method, we present the soliton solutions...

Hirota method | [formula omitted]-dimensional Konopelchenko–Dubrovsky equations | Soliton interaction | Sato theory | Solitons | (2+1)-dimensional Konopelchenko–Dubrovsky equations | SYSTEM | MATHEMATICS, APPLIED | FORM | WAVE SOLUTIONS | BACKLUND TRANSFORMATION | Konopelchenko-Dubrovsky equations | PAINLEVE ANALYSIS | MATHEMATICS | SYMBOLIC COMPUTATION | NONLINEAR EVOLUTION-EQUATIONS | (2+1)-dimensional

Hirota method | [formula omitted]-dimensional Konopelchenko–Dubrovsky equations | Soliton interaction | Sato theory | Solitons | (2+1)-dimensional Konopelchenko–Dubrovsky equations | SYSTEM | MATHEMATICS, APPLIED | FORM | WAVE SOLUTIONS | BACKLUND TRANSFORMATION | Konopelchenko-Dubrovsky equations | PAINLEVE ANALYSIS | MATHEMATICS | SYMBOLIC COMPUTATION | NONLINEAR EVOLUTION-EQUATIONS | (2+1)-dimensional

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 11/2017, Volume 74, Issue 10, pp. 2341 - 2347

Breather, lump and X soliton solutions are presented via the Hirota bilinear method, to the nonlocal (2+1)-dimensional KP equation, derived from the Alice–Bob...

[formula omitted] soliton | Alice–Bob system | Nonlocal KP equation | Lump solution | X soliton | RATIONAL SOLUTIONS | WAVE | MATHEMATICS, APPLIED | SYMMETRY | HIROTA BILINEAR EQUATION | Alice-Bob system

[formula omitted] soliton | Alice–Bob system | Nonlocal KP equation | Lump solution | X soliton | RATIONAL SOLUTIONS | WAVE | MATHEMATICS, APPLIED | SYMMETRY | HIROTA BILINEAR EQUATION | Alice-Bob system

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 10/2018, Volume 132, pp. 45 - 54

A 3 × 3 matrix spectral problem is introduced and its associated AKNS integrable hierarchy with four components is generated. From this spectral problem, a...

[formula omitted]-soliton solution | Riemann–Hilbert problem | Integrable hierarchy | N-soliton solution | MATHEMATICS | Riemann-Hilbert problem | INTEGRABLE SYSTEMS | EQUATIONS | HAMILTONIAN STRUCTURES | SEMIDIRECT SUMS | PHYSICS, MATHEMATICAL | HIERARCHY

[formula omitted]-soliton solution | Riemann–Hilbert problem | Integrable hierarchy | N-soliton solution | MATHEMATICS | Riemann-Hilbert problem | INTEGRABLE SYSTEMS | EQUATIONS | HAMILTONIAN STRUCTURES | SEMIDIRECT SUMS | PHYSICS, MATHEMATICAL | HIERARCHY

Journal Article

15.
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Riemann–Hilbert approach and N-soliton solutions for a generalized Sasa–Satsuma equation

Wave Motion, ISSN 0165-2125, 01/2016, Volume 60, pp. 62 - 72

A generalized Sasa–Satsuma equation on the line is studied via the Riemann–Hilbert approach. Firstly we derive a Lax pair associated with a 3×3 matrix spectral...

Riemann–Hilbert approach | Generalized Sasa–Satsuma equation | [formula omitted]-soliton solutions | N-soliton solutions | Generalized Sasa-Satsuma equation | Riemann-Hilbert approach | ACOUSTICS | MECHANICS | PHYSICS, MULTIDISCIPLINARY

Riemann–Hilbert approach | Generalized Sasa–Satsuma equation | [formula omitted]-soliton solutions | N-soliton solutions | Generalized Sasa-Satsuma equation | Riemann-Hilbert approach | ACOUSTICS | MECHANICS | PHYSICS, MULTIDISCIPLINARY

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 11/2017, Volume 73, pp. 136 - 142

The residual symmetry is derived for the negative-order Korteweg–de Vries equation from the truncated Painlevé expansion. This nonlocal symmetry is transformed...

Residual symmetry | Soliton-cnoidal wave interaction solution | Consistent tanh expansion method | [formula omitted]th bäcklund transformation | Negative-order KdV equation | MATHEMATICS, APPLIED | PARTIAL-DIFFERENTIAL-EQUATIONS | EVOLUTION-EQUATIONS | PAINLEVE | nth backlund transformation | Differential equations

Residual symmetry | Soliton-cnoidal wave interaction solution | Consistent tanh expansion method | [formula omitted]th bäcklund transformation | Negative-order KdV equation | MATHEMATICS, APPLIED | PARTIAL-DIFFERENTIAL-EQUATIONS | EVOLUTION-EQUATIONS | PAINLEVE | nth backlund transformation | Differential equations

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 06/2018, Volume 75, Issue 12, pp. 4221 - 4231

In this paper, a (3+1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation is investigated, which describes the dynamics of nonlinear waves in plasma...

Rogue wave solution | Breather wave solution | Dark soliton solution | The [formula omitted]-dimensional generalized Kadomtsev–Petviashvili equation | Bright soliton solution | Exact solution | The (3+1)-dimensional generalized Kadomtsev–Petviashvili equation | Water waves | Fluid dynamics | Plasma physics

Rogue wave solution | Breather wave solution | Dark soliton solution | The [formula omitted]-dimensional generalized Kadomtsev–Petviashvili equation | Bright soliton solution | Exact solution | The (3+1)-dimensional generalized Kadomtsev–Petviashvili equation | Water waves | Fluid dynamics | Plasma physics

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 02/2017, Volume 64, pp. 87 - 93

In this paper, a (2+1)-dimensional KdV equation is investigated by using the consistent Riccati expansion (CRE) method proposed by Lou (2015). It is proved...

Interaction solution | Consistent Riccati expansionmethod | [formula omitted]-dimensional KdV equation | (2+1)-dimensional KdV equation | MATHEMATICS, APPLIED | SYMMETRIES | MODEL | Consistent Riccati expansion method | BACKLUND TRANSFORMATION

Interaction solution | Consistent Riccati expansionmethod | [formula omitted]-dimensional KdV equation | (2+1)-dimensional KdV equation | MATHEMATICS, APPLIED | SYMMETRIES | MODEL | Consistent Riccati expansion method | BACKLUND TRANSFORMATION

Journal Article

Physics Letters A, ISSN 0375-9601, 2007, Volume 369, Issue 4, pp. 285 - 289

Using the Hirota bilinear method, an N-soliton solution of a ( 3 + 1 ) -dimensional nonlinear evolution equation is obtained with the aid of the perturbation...

[formula omitted]-dimensional nonlinear evolution equation | Wronskian form | Bilinear form | N-soliton solution | (3 + 1)-dimensional nonlinear evolution equation | TRANSFORMATION | PHYSICS, MULTIDISCIPLINARY | wronskian form | DE-VRIES EQUATION | (3+1)-dimensional nonlinear evolution equation | bilinear form | KORTEWEG-DEVRIES

[formula omitted]-dimensional nonlinear evolution equation | Wronskian form | Bilinear form | N-soliton solution | (3 + 1)-dimensional nonlinear evolution equation | TRANSFORMATION | PHYSICS, MULTIDISCIPLINARY | wronskian form | DE-VRIES EQUATION | (3+1)-dimensional nonlinear evolution equation | bilinear form | KORTEWEG-DEVRIES

Journal Article

Physics Letters A, ISSN 0375-9601, 2008, Volume 373, Issue 1, pp. 83 - 88

Utilizing the Hirota bilinear method, an N-soliton solution for a ( 2 + 1 ) -dimensional nonlinear evolution equation is obtained. Further, generalized double...

[formula omitted]-dimensional nonlinear evolution equation | Double Wronskian determinant | Rational solution | N-soliton solution | (2 + 1)-dimensional nonlinear evolution equation | TRANSFORMATION | PHYSICS, MULTIDISCIPLINARY | QUASI-PERIODIC SOLUTIONS | DECOMPOSITION | (2+1)-dimensional nonlinear evolution equation

[formula omitted]-dimensional nonlinear evolution equation | Double Wronskian determinant | Rational solution | N-soliton solution | (2 + 1)-dimensional nonlinear evolution equation | TRANSFORMATION | PHYSICS, MULTIDISCIPLINARY | QUASI-PERIODIC SOLUTIONS | DECOMPOSITION | (2+1)-dimensional nonlinear evolution equation

Journal Article

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