Some exact methods in the theory of nonlinear waves
Abstract
The paper reviews some methods for obtaining exact solutions to nonlinear wave problems by transformation of the original system of unknown solution to a system whose solution is in some sense easier to obtain. The application of the Backlund transformation to the nonlinear KleinGordon equation is described, showing the use of Lamb diagrams. The HopfHirota transformation is illustrated for the Burgers and the Kortewegde Vries equations. Attention is also given to the method of variation of parameters for stationary waves and to inverse methods.
 Publication:

Radiofizika
 Pub Date:
 1976
 Bibcode:
 1976RaF....19..883P
 Keywords:

 KleinGordon Equation;
 Nonlinear Equations;
 Transformations (Mathematics);
 Wave Propagation;
 Bibliographies;
 Field Theory (Physics);
 Laplace Equation;
 Liouville Equations;
 Solitary Waves;
 Traveling Waves;
 Ultrashort Pulsed Lasers;
 Variational Principles;
 Physics (General)