A symbolic algorithm for computing recursion operators of nonlinear partial differential equations
From MaRDI portal
Publication:3568448
DOI10.1080/00207160903111592zbMath1191.65166arXiv0905.2499OpenAlexW2152119681MaRDI QIDQ3568448
Douglas E. Baldwin, Willy Hereman
Publication date: 11 June 2010
Published in: International Journal of Computer Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0905.2499
inverse scattering transformsymbolic computationrecursion operatorsoliton solutionscomplete integrabilitynonlinear evolution equationnonlinear PDEsbi-Hamiltonian structuregeneralized symmetriessymbolic software
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) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)
Related Items (32)
Negative-order KdV equations in (3+1) dimensions by using the KdV recursion operator ⋮ A variety of (3 + 1)‐dimensional Burgers equations derived by using the Burgers recursion operator ⋮ A variety of \((3+1)\)-dimensional mKdV equations derived by using the mKdV recursion operator ⋮ Bäcklund transformations and soliton solutions for a \((2+1)\)-dimensional Korteweg-de Vries-type equation in water waves ⋮ Painlevé analysis for a new integrable equation combining the modified Calogero-Bogoyavlenskii-Schiff (MCBS) equation with its negative-order form ⋮ Two new integrable modified KdV equations, of third-and fifth-order, with variable coefficients: multiple real and multiple complex soliton solutions ⋮ A new integrable equation combining the modified KdV equation with the negative-order modified KdV equation: multiple soliton solutions and a variety of solitonic solutions ⋮ A variety of negative-order integrable KdV equations of higher orders ⋮ Repeated application of the recursion operator for a new hierarchy of negative-order integrable KdV equations ⋮ New soliton hierarchies associated with the real Lie algebra so(4,R) ⋮ A soliton hierarchy associated with \(\mathrm{so}(3,\mathbb R)\) ⋮ Negative-order KdV and negative-order KP equations: multiple soliton solutions ⋮ The integrable Vakhnenko-Parkes (VP) and the modified Vakhnenko-parkes (MVP) equations: multiple real and complex soliton solutions ⋮ New integrable \(\mathrm{sl}(2,\mathbb{R})\)-generalization of the classical Wadati-Konno-Ichikawa hierarchy ⋮ Computing with Hamiltonian operators ⋮ Symbolic computation of conservation laws for nonlinear partial differential equations in multiple space dimensions ⋮ Multiple complex soliton solutions for integrable negative-order KdV and integrable negative-order modified KdV equations ⋮ Conservation laws of some physical models via symbolic package GeM ⋮ \((2+1)\)-dimensional Burgers equations \(\mathrm{BE}(m+n+1)\): using the recursion operator ⋮ A spectral problem based on so$(3,\mathbb {R})$(3,R) and its associated commuting soliton equations ⋮ Recursion operators admitted by non-abelian Burgers equations: some remarks ⋮ A \((2+1)\)-dimensional time-dependent Date-Jimbo-Kashiwara-Miwa equation: Painlevé integrability and multiple soliton solutions ⋮ \((2+1)\)-dimensional mKdV (N) equations by the mKdV recursion operator: multiple soliton and multiple singular soliton solutions ⋮ Novel soliton hierarchies of Levi type and their bi-Hamiltonian structures ⋮ Negative-order modified KdV equations: multiple soliton and multiple singular soliton solutions ⋮ Negative-order integrable modified KdV equations of higher orders ⋮ Conservation laws and exact solutions of the Whitham-type equations ⋮ PDERecursionOperator ⋮ A study on the (2 + 1)-dimensional KdV4 equation derived by using the KdV recursion operator ⋮ A BASIS OF HIERARCHY OF GENERALIZED SYMMETRIES AND THEIR CONSERVATION LAWS FOR THE (3+1)-DIMENSIONAL DIFFUSION EQUATIONA ⋮ Two new integrable Kadomtsev–Petviashvili equations with time-dependent coefficients: multiple real and complex soliton solutions ⋮ New soliton hierarchies associated with the Lie algebra so(3,\(\mathbb{R}\)) and their Bi-Hamiltonian structures
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