INTEGRABLE PROPERTIES AND SIMILARITY REDUCTIONS OF THE SINE-LAPLACE EQUATION FROM AN INVISCID INCOMPRESSIBLE FLUID WITH SYMBOLIC COMPUTATION
DOI10.1142/S0217979210053628zbMath1203.37109MaRDI QIDQ4929581
Juan Li, Bo Tian, Hai-Qiang Zhang, Guang-Mei Wei
Publication date: 23 September 2010
Published in: International Journal of Modern Physics B (Search for Journal in Brave)
Symbolic computation and algebraic computation (68W30) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Solitary waves for incompressible inviscid fluids (76B25) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)
Cites Work
- Partial differential equations possessing Frobenius integrable decompositions
- The inverse scattering transform: tools for the nonlinear Fourier analysis and filtering of ocean surface waves.
- Symmetry group analysis of Benney system and an application for shallow-water equations
- Bäcklund transformations and their applications
- The solution of Navier equations of classical elasticity using Lie symmetry groups
- Regularized solution of the Cauchy problem for the Laplace equation using Meyer wavelets.
- Symmetry reductions for a dissipation-modified KdV equation
- New transformations and new approach to find exact solutions to nonlinear equations
- Similarity solutions of the Burgers equation with linear damping.
- Solitary wave transformation in a medium with sign-variable quadratic nonlinearity and cubic nonlinearity
- Revisiting Salerno's sine-Gordon model of DNA: active regions and robustness
- Direct method of solution for general boundary value problem of the Laplace equation
- On a class of preconditioners for solving the Helmholtz equation
- Construction of periodic solutions of nonlinear wave equations with Dirichlet boundary conditions by the Lindstedt series method
- Lax pair, Bäcklund transformation and \(N\)-soliton-like solution for a variable-coefficient Gardner equation from nonlinear lattice, plasma physics and ocean dynamics with symbolic computation
- Comment on: ``Spherical Kadomtsev-Petviashvili equation and nebulons for dust ion-acoustic waves with symbolic computation
- Five regimes of the quasi-cnoidal, steadily translating waves of the rotation-modified Korteweg-de Vries (Ostrovsky) equation
- Do symmetry constraints yield exact solutions?
- Spherical Kadomtsev-Petviashvili equation and nebulons for dust ion-acoustic waves with symbolic computation
- On the solitonic structures of the cylindrical dust-acoustic and dust-ion-acoustic waves with symbolic computation
- Relaxation procedures for an iterative algorithm for solving the Cauchy problem for the Laplace equation
- Macropterons, micropterons and similarity reductions for the regularized Ostrovsky-Grimshaw model for fluids and plasmas with symbolic computation
- \((2+1)\)-dimensional Broer-Kaup system of shallow water waves and similarity solutions with symbolic computation
- N-Soliton Solutions of Model Equations for Shallow Water Waves
- Nonlinear-Evolution Equations of Physical Significance
- Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
- Symbolic computation on integrable properties of a variable-coefficient Korteweg–de Vries equation from arterial mechanics and Bose–Einstein condensates
- Symbolic computation on the multi-soliton-like solutions of the cylindrical Kadomtsev–Petviashvili equation from dusty plasmas
- A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
- Relaxation in two dimensions and the ‘‘sinh-Poisson’’ equation
- The algebraic structures of isospectral Lax operators and applications to integrable equations
- ALGEBRAIC CURVES AND NON-LINEAR DIFFERENCE EQUATIONS
- On a shallow water wave equation
- Vortex Dynamics
- Soliton-like solutions of a generalized variable-coefficient higher order nonlinear Schrödinger equation from inhomogeneous optical fibers with symbolic computation
- A strong maximum principle for the Laplace equation with mixed boundary condition
This page was built for publication: INTEGRABLE PROPERTIES AND SIMILARITY REDUCTIONS OF THE SINE-LAPLACE EQUATION FROM AN INVISCID INCOMPRESSIBLE FLUID WITH SYMBOLIC COMPUTATION
