Symbolic computation and construction of soliton-like solutions for a breaking soliton equation.

DOI10.1016/S0960-0779(02)00570-2zbMath1037.81522OpenAlexW2093538068MaRDI QIDQ1416244

Biao Li, Yong Chen, Heng-Nong Xuan, Hong-Qing Zhang

Publication date: 14 December 2003

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0960-0779(02)00570-2

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51)

Related Items

New types of exact solutions for a breaking soliton equation, Construction of new soliton-like solutions of the (2 + 1) dimensional dispersive long wave equation, Construction of new soliton-like solutions for the (2 + 1) dimensional KdV equation with variable coefficients, A new variable coefficient Korteweg-de Vries equation-based sub-equation method and its application to the \((3 + 1)\)-dimensional potential-YTSF equation, New complexiton solutions of the nonlinear evolution equations using a generalized rational expansion method with symbolic computation, Periodic and solitary wave solutions of some important physical models with variable coefficients, A new Korteweg-de Vries equation-based sub-equation method and its application to the (2 + 1)-dimensional Korteweg-de Vries equation, A GENERALIZED SUB-EQUATION EXPANSION METHOD AND ITS APPLICATION TO THE NONLINEAR SCHRÖDINGER EQUATION IN INHOMOGENEOUS OPTICAL FIBER MEDIA, Exact Analytical Solutions in Bose–Einstein Condensates with Time-Dependent Atomic Scattering Length, Nonlocal symmetry and exact solutions of the \((2+1)\)-dimensional breaking soliton equation, Bifurcation and solitary-like solutions for compound KdV-Burgers-type equation, Solutions of the nonlocal (2+1)-D breaking solitons hierarchy and the negative order AKNS hierarchy, Non-travelling wave solutions to a \((3+1)\)-dimensional potential-YTSF equation and a simplified model for reacting mixtures, Application of the extended homotopy perturbation method to a kind of nonlinear evolution equations, Symbolic computation and construction of soliton-like solutions for a (2+1)-dimensional breaking soliton equation, New type of exact solutions of nonlinear evolution equations via the new sine-Poisson equation expansion method, Construction of new soliton-like solutions for the \((2+1)\) dimensional Kadomtsev-Petviashvili equation, Families of non-travelling wave solutions to a generalized variable coefficient two-dimensional KdV equation using symbolic computation, Rational approximation solution of the fractional Sharma-Tasso-Olever equation, THE RATIONAL SOLUTIONS TO A GENERALIZED RICCATI EQUATION AND THEIR APPLICATION, Bilinear Form andN-Shock-Wave Solutions for a (2+1)-Dimensional Breaking Soliton Equation in Certain Fluids with the Bell Polynomials and Auxiliary Function, Generalized extended tanh-function method and its application, Analytical solutions of the discrete nonlinear Schrödinger equation in arrays of optical fibers

Uses Software

• Maple
• ATFM

Cites Work

• Unnamed Item
• An automated \(\tanh\)-function method for finding solitary wave solutions to nonlinear evolution equations
• Extending the generalized tanh method to the generalized Hamiltonian equations: New soliton-like solutions
• Symbolic computation in engineering: Application to a breaking soliton equation
• Abundant coherent structures of the dispersive long-wave equation in \((2+1)\)-dimensional spaces.
• Explicit exact solutions for compound KdV-type and compound KdV-Burgers-type equations with nonlinear terms of any order.
• The tanh method, a simple transformation and exact analytical solutions for nonlinear reaction-diffusion equations
• Exact soliton solutions for some nonlinear partial differential equations
• Travelling solitary wave solutions to a compound KdV-Burgers equation.
• Extended tanh-function method and its applications to nonlinear equations
• Wave Propagation in Nonlinear Lattice. I
• Wave Propagation in Nonlinear Lattice. II
• New Explicit Solitary Wave Solutions and Periodic Wave Solutions for the Generalized Coupled Hirota-Satsuma KdV System
• Explicit exact solutions for new general two-dimensional KdV-type and two-dimensional KdV Burgers-type equations with nonlinear terms of any order
• Modified extended tanh-function method for solving nonlinear partial differential equations
• Generalized hyperbolic-function method with computerized symbolic computation to construct the solitonic solutions to nonlinear equations of mathematical physics
• New explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water
• A new complex line soliton for the two-dimensional KdV-Burgers equation
• New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations