Solitons on the rarefaction wave background via the Darboux transformation Journal Articles

abstract

• Rarefaction waves and dispersive shock waves are generated from the step-like initial data in many nonlinear evolution equations including the classical example of the Korteweg–de Vries (KdV) equation. When a solitary wave is injected on the step-like initial data, it is either transmitted over or trapped inside the rarefaction wave background. We show that the transmitted soliton can be obtained by using the Darboux transformation for the KdV equation. On the other hand, we show with the help of numerical simulations that the trapped soliton disappears in the long-time dynamics of the rarefaction wave.

authors

• Mucalica, Ana
• Pelinovsky, Dmitry E

status

• published 

publication date

• November 2022

has subject area

• 01 Mathematical Sciences (FoR)
• 02 Physical Sciences (FoR)
• 09 Engineering (FoR)

published in

• Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences  Journal

keywords

• DE-VRIES EQUATION
• Darboux transformation
• Korteweg-de Vries equation
• Multidisciplinary Sciences
• Science & Technology
• Science & Technology - Other Topics
• eigenvalues
• rarefaction wave
• resonant poles
• transmitted solitons
• trapped solitons

Digital Object Identifier (DOI)

• 10.1098/rspa.2022.0474

volume

• 478

issue

• 2267