Exterior differential expression of the \((1+1)\)-dimensional nonlinear evolution equation with Lax integrability

DOI10.1016/j.jmaa.2015.10.036zbMath1360.37166OpenAlexW1770116698WikidataQ115346025 ScholiaQ115346025MaRDI QIDQ892354

Chuan-Qi Su, Yi-Tian Gao, Xin Yu, Yu-Jia Shen, Long Xue

Publication date: 18 November 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2015.10.036

zbMATH Keywords

complete integrabilitynonlinear evolution equationDarboux transformationFrobenius theoremexterior differentialLax integrability

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Nonlinear evolution equations (47J35)

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Cites Work

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• Breathers and rogue waves of the fifth-order nonlinear Schrödinger equation in the Heisenberg ferromagnetic spin chain
• Rogue-wave solutions for the Kundu-Eckhaus equation with variable coefficients in an optical fiber
• \(N\)-fold Darboux transformation and solitonic interactions of a variable-coefficient generalized Boussinesq system in shallow water
• Exterior differential systems prolongations and application to a study of two nonlinear partial differential equations
• Prolongation structures of a generalized coupled Korteweg-de Vries equation and Miura transformation
• An exterior differential system for a generalized Korteweg-de Vries equation and its associated integrability
• The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains
• Conservation laws and conserved quantities for laminar two-dimensional and radial jets
• Higher-order integrable evolution equation and its soliton solutions
• A note on the prolongation structure of the cubically nonlinear integrable Camassa-Holm type equation
• Gauge transform between the first order nonisospectral AKNS hierarchy and AKNS hierarchy
• Geometric approach to soliton equations
• The KdV prolongation algebra
• Prolongation structures of nonlinear evolution equations
• Prolongation structures of nonlinear evolution equations. II
• Slowly Varying Solitary Wave Solutions of the Perturbed Korteweg‐de Vries Equation Revisited
• Direct construction method for conservation laws of partial differential equations Part I: Examples of conservation law classifications
• The gauge equivalence of the NLS and the Schrödinger flow of maps in 2 + 1 dimensions
• Fermionic covariant prolongation structure theory for supernonlinear evolution equation
• A geometric interpretation of prolongation by means of connections
• LONG NONLINEAR INTERNAL WAVES