Abstract
We study a breather’s properties within the framework of the modified Korteweg–de Vries (mKdV) model, where cubic nonlinearity is essential. Extrema, moments, and invariants of a breather with different parameters have been analyzed. The conditions in which a breather moves in one direction or another has been determined. Two limiting cases have been considered: when a breather has an N-wave shape and can be interpreted as two solitons with different polarities, and when a breather contains many oscillations and can be interpreted as an envelope soliton of the nonlinear Schrödinger equation (NLS).
Highlights
Solitons exist in various physical media, such as hydrodynamics, optics, plasma, and solids
That is why approximate approaches for a larger number of solitons, similar to the gas turbulence theory, when solitons behave like particles during collisions, began to develop simultaneously with the exact description of integrable systems using various methods
It means it has an mKdVisisa fully a fully integrable equation. It means it infinite has an number of conserved invariants, which are not affected by the soliton interaction
Summary
Solitons exist in various physical media, such as hydrodynamics, optics, plasma, and solids They are exact solutions of various integrable equations (nonlinear Schrödinger equation, equations of the Korteweg–de Vries class, etc.) and their properties have been well studied. That is why approximate approaches for a larger number of solitons, similar to the gas turbulence theory, when solitons behave like particles during collisions, began to develop simultaneously with the exact description of integrable systems using various methods (inverse problem, Darboux, Backlund, and Hirota transformations). In this case, it is called a soliton gas or soliton turbulence (in the general case of integrable turbulence).
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call