Algebraic Approaches to Partial Differential Equations

DOI10.1007/978-3-642-36874-5zbMath1273.35009arXiv1205.6535OpenAlexW1871218226MaRDI QIDQ4913585

Xiaoping Xu

Publication date: 8 April 2013

Full work available at URL: https://arxiv.org/abs/1205.6535

zbMATH Keywords

Jacobi polynomialsCalogero-Sutherland modelKP equationhypergeometric functionDavey-Stewartson equationsLegendre polynomialBoussinesq systemJacobi's elliptic functionsWeierstrass's elliptic functionsKhokhlov and Zabolotskaya equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Navier-Stokes equations (35Q30) NLS equations (nonlinear Schrödinger equations) (35Q55) Explicit solutions, first integrals of ordinary differential equations (34A05) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Solutions to PDEs in closed form (35C05) Elliptic functions and integrals (33E05) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Higher logarithm functions (33B30) Traveling wave solutions (35C07) Maxwell equations (35Q61) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (4)

Parametrically defined nonlinear differential equations and their solutions: applications in fluid dynamics ⋮ Direct functional separation of variables and new exact solutions to axisymmetric unsteady boundary-layer equations ⋮ The dispersionless Veselov-Novikov equation: symmetries, exact solutions, and conservation laws ⋮ Conformal Galilei algebras, symmetric polynomials and singular vectors

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