This is done by using a travelling wave method to formulate one-soliton solution and the finite difference method to the numerical solutions and the interactions between the solitons for the generalized nonlinear Schrodinger equations.
This achieved using a traveling wave method to formulate one-soliton solution and the P-R method is employed to the numerical solutions and the interactions between the solitons for the generalized nonlinear systems in 2-space.
This paper considers the generalized KdV equation with or without natural boundary conditions and provides a parameter region for solitons and solitary waves, and also modifies a result of Zabusky's.
As a means of establishing a soliton model based on gauge fields for hadrons, the quantum expansion method for soliton solutions recently propesed by T. D. Lee has been generalized to cover more general systems including gauge fields. Our results are similar to those obtained by T. D. Lee, but some of our quantities have a broades content, as in formula (33) - (37).
Based on a simplified model, a Sine-Gordon equation in nematic liquid cry- stals is discussed and deduced. It is shown that in liquid crystals a soliton can be created, this soliton may posses of some important biological functions.