Integrability and exact solutions of the (2+1)-dimensional KdV equation with Bell polynomials approach
DOI10.1007/s10255-022-1020-9zbMath1501.35351OpenAlexW4306774601MaRDI QIDQ2087663
Publication date: 21 October 2022
Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10255-022-1020-9
Lax pairperiodic wave solutionlump solutionbilinear formalismbilinear Bäcklund transformationsthe asymptotic properties
Asymptotic behavior of solutions to PDEs (35B40) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Integral representations of solutions to PDEs (35C15) Soliton equations (35Q51) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Soliton solutions (35C08)
Related Items (2)
Uses Software
Cites Work
- Bell polynomials approach for two higher-order KdV-type equations in fluids
- \textit{PDEBellII}: a Maple package for finding bilinear forms, bilinear Bäcklund transformations, Lax pairs and conservation laws of the KdV-type equations
- Bäcklund transformations and soliton solutions for a \((2+1)\)-dimensional Korteweg-de Vries-type equation in water waves
- The integrability of nonisospectral and variable-coefficient KdV equation with binary Bell polynomials
- New exact solutions and Bäcklund transformation for Boiti-Leon-Manna-Pempinelli equation
- The periodic problem for the Korteweg-de Vries equation
- The spectrum of Hill's equation
- On a direct procedure for the disclosure of Lax pairs and Bäcklund transformations
- Bäcklund transformation of variable-coefficient Boiti-Leon-Manna-Pempinelli equation
- Exponential polynomials
- Binary Bell polynomial manipulations on the integrability of a generalized (2+1)-dimensional Korteweg-de Vries equation
- Two new Painlevé-integrable (2+1) and (3+1)-dimensional KdV equations with constant and time-dependent coefficients
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Lax pair, conservation laws, and multi-shock wave solutions of the DJKM equation with Bell polynomials and symbolic computation
- Binary Bell polynomials and Darboux covariant Lax pairs
- A Direct Method of Calculating Periodic Wave Solutions to Nonlinear Evolution Equations. I. Exact Two-Periodic Wave Solution
- A Direct Method of Calculating Periodic Wave Solutions to Nonlinear Evolution Equations. II. Exact One- and Two-Periodic Wave Solution of the Coupled Bilinear Equations
- Integrability of the modified generalised Vakhnenko equation
- On the integrability of a generalized variable-coefficient Kadomtsev–Petviashvili equation
- EXACT ONE-PERIODIC AND TWO-PERIODIC WAVE SOLUTIONS TO HIROTA BILINEAR EQUATIONS IN (2+1) DIMENSIONS
- Periodic wave solutions of the Boussinesq equation
- Two-dimensional lumps in nonlinear dispersive systems
- N-soliton solutions to a -dimensional integrable equation
- Soliton Solutions of a Coupled Modified KdV Equations
- Construction of Bäcklund Transformations with Binary Bell Polynomials
- On a direct bilinearization method: Kaup's higher-order water wave equation as a modified nonlocal Boussinesq equation
- Integrals of nonlinear equations of evolution and solitary waves
This page was built for publication: Integrability and exact solutions of the (2+1)-dimensional KdV equation with Bell polynomials approach