A multiple exp-function method for nonlinear differential equations and its application
From MaRDI portal
Publication:3008707
DOI10.1088/0031-8949/82/06/065003zbMath1219.35209arXiv1010.3324OpenAlexW2113843433WikidataQ61891309 ScholiaQ61891309MaRDI QIDQ3008707
Yi Zhang, Wen-Xiu Ma, Tingwen Huang
Publication date: 22 June 2011
Published in: Physica Scripta (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1010.3324
Transform methods (e.g., integral transforms) applied to PDEs (35A22) Soliton equations (35Q51) Soliton solutions (35C08)
Related Items (only showing first 100 items - show all)
New extended auxiliary equation method for finding many new Jacobi elliptic function solutions of three nonlinear Schrödinger equations ⋮ The first integral method for constructing exact and explicit solutions to nonlinear evolution equations ⋮ A study on a two‐wave mode Kadomtsev–Petviashvili equation: conditions for multiple soliton solutions to exist ⋮ On traveling wave solutions of a class of KdV-Burgers-Kuramoto type equations ⋮ Integrability, conservation laws and exact solutions for a model equation under non-canonical perturbation expansions ⋮ Exact solutions of the combined Hirota-LPD equation with variable coefficients ⋮ An efficient analysis for \(N\)-soliton, lump and lump-kink solutions of time-fractional \((2+1)\)-Kadomtsev-Petviashvili equation ⋮ Unnamed Item ⋮ Two new modifications of the exp-function method for solving the fractional-order Hirota-Satsuma coupled KdV ⋮ Compacton, peakon, cuspons, loop solutions and smooth solitons for the generalized KP-MEW equation ⋮ The combination of conservation laws and auxiliary equation method ⋮ Some more solutions of Caudrey-Dodd-Gibbon equation using optimal system of Lie symmetries ⋮ The residual symmetry and exact solutions of the Davey-Stewartson III equation ⋮ Explicit Solutions and Conservation Laws of a (2+1)-dimensional KP-Joseph-Egri Equation with Power Law Nonlinearity ⋮ Logarithm transformation together with the integral bifurcation method for investigating exact solutions of the CDF equation with mKdV type ⋮ Discrete and continuum models of COVID-19 virus, formal solutions, stability and comparison with real data ⋮ An effective approach for constructing novel KP-like equations ⋮ Abundant different types of exact soliton solution to the (4+1)-dimensional Fokas and (2+1)-dimensional breaking soliton equations ⋮ Exact solutions to the fractional complex Ginzburg-Landau equation with time-dependent coefficients under quadratic-cubic and power law nonlinearities ⋮ A new integrable equation combining the modified KdV equation with the negative-order modified KdV equation: multiple soliton solutions and a variety of solitonic solutions ⋮ Novel methods for finding general forms of new multi-soliton solutions to (1+1)-dimensional KdV equation and (2+1)-dimensional Kadomtsev–Petviashvili (KP) equation ⋮ On the modified generalized multidimensional KP equation in plasma physics and fluid dynamics in \((3+1)\) dimensions ⋮ The classification of the single traveling wave solutions to the time-fraction Gardner equation ⋮ Exponential rational function method for solving nonlinear equations arising in various physical models ⋮ Time-fractional generalized Boussinesq equation for Rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions ⋮ Multiple soliton solutions of the Sawada-Kotera equation with a nonvanishing boundary condition and the perturbed Korteweg de Vries equation by using the multiple exp-function scheme ⋮ On the solution of T−controllable abstract fractional differential equations with impulsive effects ⋮ Localized spin excitations in a site-dependent antiferromagnetic spin system with d-m interaction ⋮ M-lump waves and their interactions with multi-soliton solutions for the \((3+1)\)-dimensional Jimbo-Miwa equation ⋮ Construction of abundant solutions for two kinds of \((3+1)\)-dimensional equations with time-dependent coefficients ⋮ Traveling‐wave solutions for a nonlinear non‐Ohmic cardioelectrophysiological tissue conduction cable equation ⋮ Solitonic interaction and Pfaffianization for a \((3 + 1)\)-dimensional potential Yu-Toda-Sasa-Fukuyama equation in a two-layer liquid ⋮ Kink-like excitations in a square lattice model of an antiferromagnetic spin system ⋮ Exact solutions to fractional Drinfel'd-Sokolov-Wilson equations ⋮ Conservation laws, classical symmetries and exact solutions of a (1 + 1)-dimensional fifth-order integrable equation ⋮ Explicit traveling wave solutions of five kinds of nonlinear evolution equations ⋮ Homotopy Padé method for solving second-order one-dimensional telegraph equation ⋮ On solving the (3+1)-dimensional NLEQZK equation and the (3+1)-dimensional NLmZK equation using the extended simplest equation method ⋮ Classical solution for the linear sigma model ⋮ Construction of complexiton-type solutions using bilinear form of Hirota-type ⋮ Lie symmetry analysis, optimal system, new solitary wave solutions and conservation laws of the Pavlov equation ⋮ The classification of the single traveling wave solutions to the generalized equal width equation ⋮ Exact Traveling Wave Solutions and Bifurcations of the Time-Fractional Differential Equations with Applications ⋮ Perturbational self-similar solutions for the 2-component Degasperis--Procesi system via a characteristic method ⋮ Optimal system, invariance analysis of fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation using Lie symmetry approach ⋮ Investigating one-, two-, and triple-wave solutions via multiple exp-function method arising in engineering sciences ⋮ Extended Gram-type determinant, wave and rational solutions to two (3+1)-dimensional nonlinear evolution equations ⋮ Classification of single traveling wave solutions to the nonlinear dispersion Drinfel'd-Sokolov system ⋮ The integral bifurcation method combined with factoring technique for investigating exact solutions and their dynamical properties of a generalized Gardner equation ⋮ A study on resonant multi-soliton solutions to the (2+1)-dimensional Hirota-Satsuma-Ito equations via the linear superposition principle ⋮ Exact analytical solutions for 3D-Gross-Pitaevskii equation with periodic potential by using the Kudryashov method ⋮ Extended transformed rational function method to nonlinear evolution equations ⋮ The logarithmic \((1+1)\)-dimensional KdV-like and \((2+1)\)-dimensional KP-like equations: Lie group analysis, conservation laws and double reductions ⋮ A unified analysis of exact traveling wave solutions for the fractional-order and integer-order Biswas-Milovic equation: via bifurcation theory of dynamical system ⋮ A Novel Scheme for Nonlinear Evolution Equations Using Symbolic Computations ⋮ Lie symmetries and conservation laws for a generalized \((2+1)\)-dimensional nonlinear evolution equation ⋮ On multi-soliton solutions for the \((2+1)\)-dimensional breaking soliton equation with variable coefficients in a graded-index waveguide ⋮ Exact solutions and conservation laws for a generalized improved Boussinesq equation ⋮ Integrability aspects and some abundant solutions for a new (4 + 1)-dimensional KdV-like equation ⋮ Rational wave solutions to a generalized (2+1)-dimensional Hirota bilinear equation ⋮ New exact solutions for nonlinear Atangana conformable Boussinesq-like equations by new Kudryashov method ⋮ Consistent KdV expansion method and its applications to the KP equation ⋮ Symmetry analysis and conservation laws of the Zoomeron equation ⋮ Exact solutions of the generalized (2+1)-dimensional BKP equation by the \(G'/G\)-expansion method and the first integral method ⋮ Novel solitary wave solutions for the \((3+1)\)-dimensional extended Jimbo-Miwa equations ⋮ EXACT SOLUTIONS FOR A DIRAC-TYPE EQUATION WITH N-FOLD DARBOUX TRANSFORMATION ⋮ Observations on the class of ``Balancing Principle for nonlinear PDEs that can be treated by the auxiliary equation method ⋮ Dromion-like structures in the variable coefficient nonlinear Schrödinger equation ⋮ A GENERALIZED METHOD AND ITS APPLICATIONS TO n-DIMENSIONAL FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS IN FRACTAL DOMAIN ⋮ Algebraic Traveling Wave Solutions to Nonlinear Evolution Equations ⋮ A generalized (2 + 1)-dimensional Calogaro-Bogoyavlenskii-Schiff equation: symbolic computation, symmetry reductions, exact solutions, conservation laws ⋮ Microtubules nonlinear models dynamics investigations through the \(\exp(-\Phi(\xi))\)-expansion method implementation ⋮ New rogue waves and dark-bright soliton solutions for a coupled nonlinear Schrödinger equation with variable coefficients ⋮ New hyperbolic function solutions for some nonlinear partial differential equation arising in mathematical physics ⋮ On the solutions and conservation laws of a two-dimensional Korteweg de Vries model: multiple \(\exp\)-function method ⋮ Extended generalized \((Zakh\frac{G'}{G})\)-expansion method for solving the nonlinear quantum Zakharov-Kuznetsov equation ⋮ New solitary wave solutions for two nonlinear evolution equations ⋮ Extended transformed rational function method and applications to complexiton solutions ⋮ Interaction between kink solitary wave and rogue wave for \((2+1)\)-dimensional Burgers equation ⋮ Soliton and Riemann theta function quasi-periodic wave solutions for a \((2+1)\)-dimensional generalized shallow water wave equation ⋮ Soliton solutions of Davey-Stewartson equation by trial equation method and ansatz approach ⋮ Optical solitons with Biswas-Milovic equation for power law and dual-power law nonlinearities ⋮ Solitons and other solutions to Boussinesq equation with power law nonlinearity and dual dispersion ⋮ Bäcklund transformation and \(N\)-shock-wave solutions for a (3+1)-dimensional nonlinear evolution equation ⋮ Explicit solutions for the \((2+1)\)-dimensional Jaulent-Miodek equation using the integrating factors method in an unbounded domain ⋮ Exact propagating multi-anti-kink soliton solutions of a \((3+1)\)-dimensional B-type Kadomtsev-Petviashvili equation ⋮ Exact three-wave solutions for the \((3+1)\)-dimensional Boiti-Leon-Manna-Pempinelli equation ⋮ Modified method of simplest equation for obtaining exact solutions of the Zakharov-Kuznetsov equation, the modified Zakharov-Kuznetsov equation, and their generalized forms ⋮ Analytical study of solitons to nonlinear time fractional parabolic equations ⋮ Multiple-soliton solutions, soliton-type solutions and rational solutions for the \((3+1)\)-dimensional generalized shallow water equation in oceans, estuaries and impoundments ⋮ Mixed lump-kink solutions to the KP equation ⋮ A new simplified bilinear method for the \(N\)-soliton solutions for a generalized FmKdV equation with time-dependent variable coefficients ⋮ The periodic solutions to Kawahara equation by means of the auxiliary equation with a sixth-degree nonlinear term ⋮ A direct Bäcklund transformation for a (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq-like equation ⋮ Painlevé integrability and new exact solutions of the \((4 + 1)\)-dimensional Fokas equation ⋮ Frobenius' idea together with integral bifurcation method for investigating exact solutions to a water wave model of the generalized mKdV equation ⋮ Symmetry analysis and conservation laws of a generalized two-dimensional nonlinear KP-MEW equation ⋮ Solitary and periodic wave solutions of Calogero-Bogoyavlenskii-Schiff equation via exp-function methods ⋮ Solving the \((3+1)\)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm ⋮ Determinant solutions to a \((3+1)\)-dimensional generalized KP equation with variable coefficients
Uses Software
This page was built for publication: A multiple exp-function method for nonlinear differential equations and its application
