Nonlinear dispersion equations: smooth deformations, compactons, and extensions to higher orders

Abstract

Third-order nonlinear dispersion equations (NDEs) are shown to admit both shock and rarefaction waves (as weak solutions), which are distinguished by a smooth deformation approach. Compacton-type travelling wave solutions are proved to be both delta-entropy and G-admissible (in the sense of I.M. Gel'fand, 1963). Extensions to some higher-order NDEs are performed.

39 pages, 17 figures

References in corpus (2)

• Formation of shocks in higher-order nonlinear dispersion PDEs: nonuniqueness and nonexistence of entropy
• Third-order nonlinear dispersion PDEs: shocks, rarefaction, and blow-up waves

Cited by in corpus (3)

• Formation of shocks in higher-order nonlinear dispersion PDEs: nonuniqueness and nonexistence of entropy
• Very Singular Similarity Solutions and Hermitian Spectral Theory for Semilinear Odd-Order PDEs
• On blow-up shock waves for a nonlinear PDE associated with Euler equations