The Riquier-Janet theory and its application to nonlinear evolution equations

DOI10.1016/0167-2789(84)90447-0zbMath0588.58032OpenAlexW2030668472MaRDI QIDQ1073416

Fritz Schwarz

Publication date: 1984

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(84)90447-0

zbMATH Keywords

Bäcklund transformationsnonlinear evolution equationsintegrability conditionssystem of partial differential equationscomputer algebra system REDUCEprolongation of Estabrook and Wahlquist

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Partial differential equations of mathematical physics and other areas of application (35Q99) Discrete mathematics in relation to computer science (68R99)

Related Items

Review of symbolic software for Lie symmetry analysis ⋮ DIMSYM and LIE: Symmetry determination packages ⋮ Computer algebra determination of symmetries in general relativity ⋮ Reduction of systems of nonlinear partial differential equations to simplified involutive forms ⋮ Term-ordering free involutive bases ⋮ Intertwining Laplace Transformations of Linear Partial Differential Equations ⋮ Involutive characteristic sets of algebraic partial differential equation systems ⋮ Involutive directions and new involutive divisions ⋮ Formal solutions of differential equations

Uses Software

• REDUCE

Cites Work

• The Estabrook-Wahlquist method with examples of application
• Non-abelian prolongations and complete integrability
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• Prolongation structures of nonlinear evolution equations
• When Nonlinear Differential Equations are Equivalent to Linear Differential Equations
• Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation
• The partial differential equation u_t + uu_x = μ_xx
• Unnamed Item
• Unnamed Item
• Unnamed Item