A direct algorithm of one-dimensional optimal system for the group invariant solutions

Abstract

A direct and systematic algorithm is proposed to find one-dimensional optimal system for the group invariant solutions, which is attributed to the classification of its corresponding one-dimensional Lie algebra. Since the method is based on different values of all the invariants, the process itself can both guarantee the comprehensiveness and demonstrate the inequivalence of the optimal system, with no further proof. To illustrate our method more clearly , we give a couple of well-known examples: the Korteweg-de Vries (KdV) equation and the heat equation.

12 pages

References in corpus (1)

• Group Analysis of the Novikov Equation

Cited by in corpus (5)

• One-dimensional optimal system for 2D Rotating Ideal Gas
• Lie symmetries and similarity solutions for rotating shallow water
• On invariant analysis and conservation laws for degenerate coupled multi-KdV equations for multiplicity l = 3
• Nonlocal symmetries and conservation laws of the coupled Hirota equation
• Exact Anti-Self-Dual four-manifolds with a Killing symmetry by similarity transformations