Integral bifurcation method together with a translation-dilation transformation for solving an integrable 2-component Camassa-Holm shallow water system
DOI10.1155/2012/736765zbMath1267.35024OpenAlexW2123087434WikidataQ58907260 ScholiaQ58907260MaRDI QIDQ1952924
Publication date: 3 June 2013
Published in: Journal of Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1155/2012/736765
solitary wavecompacton solutionsloop solitonsingular periodic wavekink wavesmooth periodic wavesingular waveperiodic kink wave
PDEs in connection with fluid mechanics (35Q35) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Bifurcations in context of PDEs (35B32) Traveling wave solutions (35C07) Soliton solutions (35C08)
Related Items
Cites Work
- Unnamed Item
- Perturbational blowup solutions to the 2-component Camassa-Holm equations
- Attractor for the viscous two-component Camassa-Holm equation
- Persistence properties and unique continuation of solutions to a two-component Camassa-Holm equation
- Exact traveling wave solutions of explicit type, implicit type, and parametric type for \(K(m, n)\) equation
- Deformations of semisimple bihamiltonian structures of hydrodynamic type
- Some new soliton-like solutions and periodic wave solutions with loop or without loop to a generalized KdV equation
- The geometry of the two-component Camassa-Holm and Degasperis-Procesi equations
- Global weak solutions for a two-component Camassa-Holm shallow water system
- Approximate damped oscillatory solutions for generalized KdV-Burgers equation and their error estimates
- Asymptotic profiles of solutions to the two-component Camassa-Holm system
- On an integrable two-component Camassa-Holm shallow water system
- Wave breaking for a modified two-component Camassa-Holm system
- Blow-up criteria of solutions to a modified two-component Camassa-Holm system
- On smooth traveling waves of an integrable two-component Camassa-Holm shallow water system
- The integral bifurcation method and its application for solving a family of third-order dispersive PDEs
- Global existence and blow-up phenomena for an integrable two-component Camassa-Holm shallow water system
- On the global existence and wave-breaking criteria for the two-component Camassa-Holm system
- An algebraic method exactly solving two high-dimensional nonlinear evolution equations
- Periodic and solitary-wave solutions of the Degasperis-Procesi equation
- On solitons, compactons, and Lagrange maps.
- A 2-component or \(N=2\) supersymmetric Camassa-Holm equation
- A two-component generalization of the Camassa-Holm equation and its solutions
- Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation
- The extended \(F\)-expansion method and its application for solving the nonlinear wave, CKGZ, GDS, DS and GZ equations
- Explicit solutions of the Camassa-Holm equation
- Bifurcations of travelling wave solutions for a two-component Camassa-Holm equation
- Blow-up and global solutions to a new integrable model with two components
- On Solutions to a Two-Component Generalized Camassa-Holm Equation
- Extended Camassa-Holm Hierarchy and Conserved Quantities
- Stability of Solitary Waves and Wave-Breaking Phenomena for the Two-Component Camassa-Holm System
- A derivation of equations for wave propagation in water of variable depth
- On second grade fluids with vanishing viscosity
- Camassa–Holm, Korteweg–de Vries-5 and other asymptotically equivalent equations for shallow water waves
- The Camassa–Holm equation for water waves moving over a shear flow
- An integrable shallow water equation with peaked solitons
- Camassa–Holm, Korteweg–de Vries and related models for water waves
- The interaction of the ω-soliton and ω-cuspon of the Camassa–Holm equation
- Integral bifurcation method combined with computer for solving a higher order wave equation of KdV type
- Smooth and non-smooth traveling waves in a nonlinearly dispersive equation
- Exact travelling-wave solutions of an integrable equation arising in hyperelastic rods.