Solitary Wave Interactions In Dispersive Equations Using Manton's Approach

Abstract

We generalize the approach first proposed by Manton [Nuc. Phys. B {\bf 150}, 397 (1979)] to compute solitary wave interactions in translationally invariant, dispersive equations that support such localized solutions. The approach is illustrated using as examples solitons in the Korteweg-de Vries equation, standing waves in the nonlinear Schr{ö}dinger equation and kinks as well as breathers of the sine-Gordon equation.

5 pages, 4 figures, slightly modified version to appear in Phys. Rev. E

References in corpus (4)

• Discrete Breathers
• A Potential of Interaction between Two- and Three-Dimensional Solitons
• Localized breathing solutions for Bose-Einstein condensates in periodic traps
• Coherent Collisions between Bose-Einstein Condensates

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• Multi-kink scattering in the double sine-Gordon model
• Interactions and dynamics of one-dimensional droplets, bubbles and kinks
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• Supersolidity of cnoidal waves in an ultracold Bose gas
• Topological defects with power-law tails
• Stability and dynamics of nonlinear excitations in a two-dimensional droplet-bearing environment
• Scattering of kinks in the $B{\phi }^4$ model
• Interactions of solitary waves in the Adlam-Allen model