SOLITARY AND E-SHOCK WAVES IN A RESONANT SYSTEM BETWEEN LONG AND SHORT WAVES

In order to examine solitary and E-shock waves in a resonant system be tween long and short waves, a reduced set of ordinary differential equ ations (ODEs) are considered by a simple traveling-wave transformation . It is then shown that analytical solutions can be obtained systemati cally by means of the modified Hirota's method. A variety of numerical solutions including oscillatory solitary and E-shock waves are also f ound for various values of the parameters. In particular, characterist ic properties of the solutions are examined for the case when the ODEs hold the Painleve property. In this connection, integrability of the original partial differential equations (PDEs) in the nearly integrabl e region is discussed together with the Lyapunov exponent for the soli ton-like solutions.