The observation that the soliton-like solutions of a given second-order nonlinear differential equation define the separatrix of the equivalent autonomous system is used to obtain the one-soliton solutions for theφ4 theories (the usual and the one with the wrong sign of the mass term), theφ6, theφ8, the sine-Gordon theories and the KdV equation. Transformations are given which transform the sine-Gordon equation into an equation belonging to theφ2n class of theories. A procedure is evolved for obtaining the two-soliton solutions for the sine-Gordon theory without the use of Backlund transformations; it is suggested that this procedure may be useful for investigating the existence of similar solutions for theories of the polynomial type.
Volume 96, 2022
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