General soliton and (semi-)rational solutions of the partial reverse space y-non-local Mel’nikov equation with non-zero boundary conditions
Open Access
- 7 April 2021
- journal article
- research article
- Published by The Royal Society in Royal Society Open Science
- Vol. 8 (4)
- https://doi.org/10.1098/rsos.201910
Abstract
General soliton and (semi-)rational solutions to the y-non-local Mel’nikov equation with non-zero boundary conditions are derived by the Kadomtsev–Petviashvili (KP) hierarchy reduction method. The solutions are expressed in N × N Gram-type determinants with an arbitrary positive integer N. A possible new feature of our results compared to previous studies of non-local equations using the KP reduction method is that there are two families of constraints among the parameters appearing in the solutions, which display significant discrepancies. For even N, one of them only generates pairs of solitons or lumps while the other one can give rise to odd numbers of solitons or lumps; the interactions between lumps and solitons are always inelastic for one family whereas the other family may lead to semi-rational solutions with elastic collisions between lumps and solitons. These differences are illustrated by a thorough study of the solution dynamics for N = 1, 2, 3. Besides, regularities of solutions are discussed under proper choices of parameters.Funding Information
- National Natural Science Foundation of China (11701382, 11971288)
This publication has 42 references indexed in Scilit:
- Nonlinear waves in-symmetric systemsReviews of Modern Physics, 2016
- Towards a gauge-equivalent magnetic structure of the nonlocal nonlinear Schrödinger equationPhysical Review A, 2016
- Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equationNonlinearity, 2016
- Observation of PT phase transition in a simple mechanical systemAmerican Journal of Physics, 2013
- Integrable Nonlocal Nonlinear Schrödinger EquationPhysical Review Letters, 2013
- Parity–time synthetic photonic latticesNature, 2012
- Experimental observation of the dual behavior of-symmetric scatteringPhysical Review A, 2012
- Families of Particles with Different Masses in PT-Symmetric Quantum Field TheoryPhysical Review Letters, 2010
- Observation of parity–time symmetry in opticsNature Physics, 2010
- Real Spectra in Non-Hermitian Hamiltonians HavingSymmetryPhysical Review Letters, 1998