Abstract
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 theφ 4 theories (the usual and the one with the wrong sign of the mass term), theφ 6, theφ 8, the sine-Gordon theories and the KdV equation. Transformations are given which transform the sine-Gordon equation into an equation belonging to theφ 2n 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.
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Malik, G.P., Subba Rao, J. & Johri, G. Soliton-like solutions of some nonlinear theories and transformations among them. Pramana - J Phys 20, 429–438 (1983). https://doi.org/10.1007/BF02875505
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DOI: https://doi.org/10.1007/BF02875505