On the class of nonlinear PDEs that can be treated by the modified method of simplest equation. Application to generalized Degasperis-Processi equation and \(b\)-equation
From MaRDI portal
Publication:551081
DOI10.1016/j.cnsns.2010.11.013zbMath1229.35028arXiv1304.1164OpenAlexW1967473206MaRDI QIDQ551081
Nikolay K. Vitanov, Kaloyan N. Vitanov, Zlatinka I. Dimitrova
Publication date: 13 July 2011
Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1304.1164
Solutions to PDEs in closed form (35C05) Other special methods applied to PDEs (35A25) Traveling wave solutions (35C07)
Related Items (13)
The explicit periodic wave solutions and their limit forms for a generalized \(b\)-equation ⋮ Population dynamics in presence of state dependent fluctuations ⋮ On the wave solutions of two-mode equations ⋮ On traveling waves in lattices: the case of Riccati lattices ⋮ Deep-water waves: on the nonlinear Schrödinger equation and its solutions ⋮ Traveling waves and statistical distributions connected to systems of interacting populations ⋮ New abundant solitary wave structures for a variety of some nonlinear models of surface wave propagation with their geometric interpretations ⋮ B-class solitary waves and their persistence under Kuramoto-Sivashinsky perturbation ⋮ Explicit exact solutions of some nonlinear evolution equations with their geometric interpretations ⋮ On modified method of simplest equation for obtaining exact and approximate solutions of nonlinear PDEs: The role of the simplest equation ⋮ New exact solutions for Kudryashov-Sinelshchikov equation ⋮ Modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations: further development of the methodology with applications ⋮ On solitary wave solutions of a class of nonlinear partial differential equations based on the function \(1/ \cosh^n(\alpha x + \beta t)\)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A transformed rational function method and exact solutions to the \(3+1\) dimensional Jimbo-Miwa equation
- Be careful with the Exp-function method
- On nonlinear dynamics of interacting populations: coupled kink waves in a system of two populations
- Seven common errors in finding exact solutions of nonlinear differential equations
- Modified method of simplest equation: powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs
- Application of simplest equations of Bernoulli and Riccati kind for obtaining exact traveling-wave solutions for a class of PDEs with polynomial nonlinearity
- Application of the method of simplest equation for obtaining exact traveling-wave solutions for two classes of model PDEs from ecology and population dynamics
- Exact solutions for the generalized sine-Gordon and the generalized sinh-Gordon equations
- Chaotic pairwise competition
- Exact solitary waves of the Fisher equation
- Exp-function method for nonlinear wave equations
- Modified method of simplest equation and its application to nonlinear PDEs
- Influence of adaptation on the nonlinear dynamics of a system of competing populations
- On nonlinear population waves
- Explicit solutions of Fisher's equation for a special wave speed
- Complexiton solutions to the Korteweg-de Vries equation
- Upper bounds on the heat transport in a porous layer
- Extended simplest equation method for nonlinear differential equations
- Analytical and numerical investigation of two families of Lorenz-like dynamical systems
- Simplest equation method to look for exact solutions of nonlinear differential equations
- Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation
- The tanh method: exact solutions of the sine-Gordon and the sinh-Gordon equations
- Extended tanh-function method and its applications to nonlinear equations
- Symmetry analysis and exact solutions of the 2+1 dimensional sine-Gordon system
- Dynamical consequences of adaptation of the growth rates in a system of three competing populations
- Nonlinear-Evolution Equations of Physical Significance
- Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
- Painlevé Tests, Singularity Structure and Integrability
- The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
- Breather and soliton wave families for the sine–Gordon equation
- The (2 + 1)-dimensional sine - Gordon equation; integrability and localized solutions
- On travelling waves and double-periodic structures in two-dimensional sine - Gordon systems
- Method for Solving the Korteweg-deVries Equation
- Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions
- New class of running-wave solutions of the (2+1)-dimensional sine-Gordon equation
- Symmetries and exact solutions of a (2+1)-dimensional sine-Gordon system
- Water waves and integrability
- The Classical Problem of Water Waves: a Reservoir of Integrable and Nearly-Integrable Equations
- Adaptation and its impact on the dynamics of a system of three competing populations
- New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations
This page was built for publication: On the class of nonlinear PDEs that can be treated by the modified method of simplest equation. Application to generalized Degasperis-Processi equation and \(b\)-equation
