On the soliton, invariant, and shock solutions of a fourth-order nonlinear equation
Abstract
A fourth-order nonlinear partial differential equation is derived from the analysis of an infinitely long transmission line composed of distributed sections and containing a nonlinear capacitance. The equation permits the propagation of solitary waves and admits an invariant (similar) solution under the spiral group. Results from an experimental transmission line demonstrate that two implicit traveling wave solutions permit the evolution of a discontinuity in the first derivatives (shocks).
- Publication:
-
Journal of Mathematical Analysis and Applications
- Pub Date:
- December 1975
- Bibcode:
- 1975JMAA...52..538L
- Keywords:
-
- Nonlinear Equations;
- Shock Discontinuity;
- Solitary Waves;
- Transmission Lines;
- Wave Equations;
- Wave Propagation;
- Capacitance;
- Invariance;
- P-N Junctions;
- Partial Differential Equations;
- Traveling Waves;
- Electronics and Electrical Engineering