Lie symmetry, nonlocal symmetry analysis, and interaction of solutions of a \((2+1)\)-dimensional KdV-mKdV equation
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Publication:2036331
DOI10.1134/S0040577921020033zbMath1467.35297MaRDI QIDQ2036331
Publication date: 29 June 2021
Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)
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) Applications of Lie algebras and superalgebras to integrable systems (17B80) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Soliton solutions (35C08)
Related Items (8)
A NEW (3+1)-DIMENSIONAL KDV EQUATION AND MKDV EQUATION WITH THEIR CORRESPONDING FRACTIONAL FORMS ⋮ Symmetry-preserving difference models of some high-order nonlinear integrable equations ⋮ Nonlocal symmetries and solutions of the \((2+1)\) dimension integrable Burgers equation ⋮ M-lump solutions to the \((2+1)\)-dimensional generalized Calogero-Bogoyavlenshii-Schiff equation ⋮ On reducing and finding solutions of nonlinear evolutionary equations via generalized symmetry of ordinary differential equations ⋮ Reverse-time type nonlocal Sasa–Satsuma equation and its soliton solutions ⋮ Numerical simulation of a generalized nonlinear derivative Schrödinger equation ⋮ Lump solution, breather soliton and more soliton solutions for a \((2 + 1)\)-dimensional generalized Benjamin-Ono equation
Cites Work
- Multi-symplectic method for the generalized (2+1)-dimensional KdV-mKdV equation
- Consistent Riccati expansion solvability and soliton-cnoidal wave interaction solution of a \((2 + 1)\)-dimensional Korteweg-de Vries equation
- Study of lump dynamics based on a dimensionally reduced Hirota bilinear equation
- Nonlocal symmetry, Darboux transformation and soliton-cnoidal wave interaction solution for the shallow water wave equation
- On traveling wave solutions to combined KdV-mKdV equation and modified Burgers-KdV equation
- Similarity and symmetry methods. Applications in elasticity and mechanics of materials. Lecture notes given at the EUROMECH workshop `Similarity, symmetry and group theoretical methods in mechanics, Varna, Bulgaria, June 6--9, 2013
- Nonlocally related systems, linearization and nonlocal symmetries for the nonlinear wave equation
- Applications of symmetry methods to partial differential equations
- Symmetry and integration methods for differential equations
- Nonlocal symmetry, CRE solvability and soliton-cnoidal solutions of the \((2+1)\)-dimensional modified KdV-Calogero-Bogoyavlenkskii-Schiff equation
- Lump solutions to nonlinear partial differential equations via Hirota bilinear forms
- Bäcklund transformations, rational solutions and soliton-cnoidal wave solutions of the modified Kadomtsev-Petviashvili equation
- Lie symmetries for systems of evolution equations
- Abundant lumps and their interaction solutions of \((3+1)\)-dimensional linear PDEs
- CK transformations, symmetries, exact solutions and conservation laws of the generalized variable-coefficient KdV types of equations
- New interaction solutions from residual symmetry reduction and consistent Riccati expansion of the \((2+1)\)-dimensional Boussinesq equation
- Symmetry reductions and exact solutions to the systems of carbon nanotubes conveying fluid
- Interaction behavior associated with a generalized \((2+1)\)-dimensional Hirota bilinear equation for nonlinear waves
- Symmetry reduction related with nonlocal symmetry for Gardner equation
- Lie symmetry analysis of the Heisenberg equation
- Painlevé analysis and exact solutions of the fourth-order equation for description of nonlinear waves
- Localized excitations and interactional solutions for the reduced Maxwell-Bloch equations
- Multiple lump solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation
- Conservation laws and nonlocally related systems of the Hunter-Saxton equation for liquid crystal
- Lump solutions to the Kadomtsev-Petviashvili equation
- The \((2+1)\)-dimensional Konopelchenko-Dubrovsky equation: nonlocal symmetries and interaction solutions
- Residual symmetry, Bäcklund transformation and CRE solvability of a \((2+1)\)-dimensional nonlinear system
- New exact solutions of \((2+1)\)-dimensional Gardner equation via the new sine-Gordon equation expansion method
- A numerical application of the decomposition method for the combined KdV-MKdV equation
- Decomposition of the (2 + 1)- dimensional Gardner equation and its quasi-periodic solutions
- Nonlocal symmetries related to Bäcklund transformation and their applications
- Framework for potential systems and nonlocal symmetries: Algorithmic approach
- Inverse spectral transform for the (2 + 1)-dimensional Gardner equation
- Exact solutions to the combined KdV and mKdV equation
- Nonlocal symmetries classifications and exact solution of Chaplygin gas equations
- Lie symmetry analysis, Bäcklund transformations, and exact solutions of a (2 + 1)-dimensional Boiti-Leon-Pempinelli system
- BREAKING SOLITONS. III
- Consistent Riccati Expansion for Integrable Systems
- Exact solutions to the combined KdV–mKdV equation by the extended mapping method
- A symmetry-based method for constructing nonlocally related partial differential equation systems
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