Multidimensional hierarchies of (1+1)-dimensional integrable partial differential equations. Nonsymmetric ∂̄-dressing
From MaRDI portal
Publication:2738184
DOI10.1063/1.1286985zbMath0979.35124OpenAlexW1994234089MaRDI QIDQ2738184
Publication date: 30 August 2001
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.1286985
\(\overline{\partial}\)-problemmultidimensional integrable partial differential equationsnonsymmetric dressing
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Soliton equations (35Q51) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)
Related Items
On the dressing method in multidimension ⋮ Combination of Inverse Spectral Transform Method and Method of Characteristics: Deformed Pohlmeyer Equation ⋮ The spectral problem and particular solutions to the \((2+1)\)-dimensional integrable generalization of the Camassa-Holm equation ⋮ Families of particular solutions to multidimensional partial differential equations
Cites Work
- On a class of physically important integrable equations
- The reduction problem and the inverse scattering method
- Symplectic structures, their Bäcklund transformations and hereditary symmetries
- Construction of higher-dimensional nonlinear integrable systems and of their solutions
- Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II
- Generalization of the inverse scattering problem method
- The Euler-Poincaré equations and semidirect products with applications to continuum theories
- Some generalizations of the two-dimensional Toda chain and sinh-Gordon equations
- The geometry of peaked solitons and billiard solutions of a class of integrable PDE's
- Dual \(\overline\partial\)-problem, \((2+1)\)-dimensional integrable nonlinear evolution equations and their reductions
- Two-dimensional integrable generalization of the Camassa-Holm equation
- The non-local delta problem and (2+1)-dimensional soliton equations
- Wave solutions of a (2+1)-dimensional generalization of the nonlinear Schr dinger equation
- The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
- On the simplest (2+1) dimensional integrable spin systems and their equivalent nonlinear Schrödinger equations
- Multicomponent equations associated to non-isospectral scattering problems
- An integrable shallow water equation with peaked solitons
- Motion of curves and surfaces and nonlinear evolution equations in (2+1) dimensions
- Breaking solitons in 2+1-dimensional integrable equations
- On the link between umbilic geodesics and soliton solutions of nonlinear PDEs
- Camassa-Holm equation: transformation to deformed sinh-Gordon equations, cuspon and soliton solutions