Conditional symmetry of equations of nonlinear mathematical physics

DOI10.1007/BF01067273zbMath0763.35086OpenAlexW2161404885MaRDI QIDQ1185170

W. I. Fushchich

Publication date: 28 June 1992

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01067273

zbMATH Keywords

solutionsheat transferreductioninvariance principleDiracMaxwellSchrödingerd'AlembertKorteweg-de VriesBoussinesqlinearization of equationsaccoustics

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Invariance and symmetry properties for PDEs on manifolds (58J70)

Related Items (10)

Conditional symmetries of nonlinear third-order ordinary differential equations ⋮ Solutions of first-order quasilinear systems expressed in Riemann invariants ⋮ Subsymmetries and their properties ⋮ Differential Equations Invariant Under Conditional Symmetries ⋮ Nonclassical reductions of a \((3+1)\)-cubic nonlinear Schrödinger system ⋮ Construction of Partial Differential Equations with Conditional Symmetries ⋮ Nonlocal ansätze, reduction and some exact solutions for the system of the van der Waals equations ⋮ All solutions of standard symmetric linear partial differential equations have classical Lie symmetry ⋮ Nonclassical symmetry reductions of the Boussinesq equation ⋮ Multimode solutions of first-order elliptic quasilinear systems

Cites Work

• Symmetry and exact solutions of multidimensional nonlinear wave equations
• Group properties of u//(tt)=[f(u)u//x//x]
• The construction of special solutions to partial differential equations
• Non-classical symmetry reduction: example of the Boussinesq equation
• New similarity reductions of the Boussinesq equation
• On the reduction and some new exact solutions of the nonlinear Dirac and Dirac-Klein-Gordon equations
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