The interaction between nonlinear Schrijdinger solitons is derived by the least action principle approach as a potential function of the soliton's separation and their initial relative phase, which shows clearly how the solitons interact with each other. Two solitons with the same initial phase always attract each other, while those of opposite phase repel. The method developed in this paper can be extended t o deal with interaction between solitons of other nonlinear equations.
Using the perturbation method and by means of a general mathematics technique similar to the variation of constant, we present mainly some relative oscillation solution for the damping Sine-Gordon equation under certain conditions. And a t the end of this paper, we give two so-called critical speeds of traveling wave. There is an interesting relationship about value and ordering of the two critical speeds.
In this paper we shall examine the correlations among tlw external./ioce, variable dampblg and variable restor#lg /brce. Some new results are obtained.
The ezpression of non-propagating solitary waves within the fluid in a rectangular trough has been obtained using the method of multiple scales, from which we can understand the picture of motion everywhere in fluid.
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