Journal
MODERN PHYSICS LETTERS B
Volume 35, Issue 32, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0217984921504832
Keywords
Modified KdV hierarchy; nonzero boundary conditions; Riemann-Hilbert problem; multi-triple-pole solitons and breathers
Funding
- NSFC [11925108, 11731014]
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This paper presents general triple-pole multi-soliton solutions for the focusing mKdV equation with nonzero boundary conditions and triple zeros of analytical scattering coefficients using the inverse scattering transform. The obtained solutions can also be degenerated to triple-pole soliton solutions with zero boundary conditions. Moreover, the analysis includes representative reflectionless potentials containing triple-pole multi-dark-anti-dark solitons and breathers.
In this paper, the general triple-pole multi-soliton solutions are proposed for the focusing modified Korteweg-de Vries (mKdV) equation with both nonzero boundary conditions (NZBCs) and triple zeros of analytical scattering coefficients by means of the inverse scattering transform. Furthermore, we also give the corresponding trace formulae and theta conditions. Particularly, we analyze some representative reflectionless potentials containing the triple-pole multi-dark-anti-dark solitons and breathers. The idea can also be extended to the whole mKdV hierarchy (e.g. the fifth-order mKdV equation, and third-fifth-order mKdV equation) with NZBCs and triple zeros of analytical scattering coefficients. Moreover, these obtained triple-pole solutions can also be degenerated to the triple-pole soliton solutions with zero boundary conditions.
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