PT-symmetric nonlocal Davey-Stewartson I equation: General lump-soliton solutions on a background of periodic line waves

Abstract We study the general lump-type soliton solutions on a background of periodic line waves in the P T -symmetric nonlocal Davey–Stewartson I (DS I) equation. By using the Kadomtsev–Petviashvili hierarchy reduction method, new families of semi-rational solutions termed as lump-soliton solutions to the nonlocal DS I equation are constructed. Under particular parameters restrictions we obtain: (a) different types of lumps sitting on a background of periodic line waves and (b) different types of lumps interacting with line solitons on a background of periodic line waves. The interactions of lumps and line solitons are inelastic, generating three generic dynamical scenarios: (i) lumps fusing into line solitons, (ii) lumps fissioning from line solitons, and (iii) a combined process consisting of lumps fusing into and fissioning from line solitons.

[1]  Xiao Deng,et al.  Solutions of Nonlocal Equations Reduced from the AKNS Hierarchy , 2018 .

[2]  M. Jimbo,et al.  TRANSFORMATION GROUPS FOR SOLITON EQUATIONS , 1982 .

[3]  Amarendra K. Sarma,et al.  Peregrine rogue wave dynamics in the continuous nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity , 2015, Commun. Nonlinear Sci. Numer. Simul..

[4]  Asli Pekcan,et al.  Nonlocal Nonlinear Schr\"odinger Equations and Their Soliton Solutions , 2017, 1707.07610.

[5]  J. Rao,et al.  PT-symmetric nonlocal Davey–Stewartson I equation: Soliton solutions with nonzero background , 2020 .

[6]  J. Rao,et al.  Rational and Semirational Solutions of the Nonlocal Davey–Stewartson Equations , 2017, 1704.06792.

[7]  C. Bender,et al.  Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry , 1997, physics/9712001.

[8]  A. S. Fokas,et al.  Integrable multidimensional versions of the nonlocal nonlinear Schrödinger equation , 2016 .

[9]  Jianke Yang,et al.  Nonlinear waves in PT -symmetric systems , 2016, 1603.06826.

[10]  Zixiang Zhou.  Darboux Transformations and Global Explicit Solutions for Nonlocal Davey–Stewartson I Equation , 2016, 1612.05689.

[11]  Pei Lv,et al.  Explicit solutions to a nonlocal 2-component complex modified Korteweg-de Vries equation , 2020, Appl. Math. Lett..

[12]  M. Ablowitz,et al.  Integrable Nonlocal Nonlinear Equations , 2016, 1610.02594.

[13]  Yasuhiro Ohta,et al.  General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation , 2011, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[14]  Yuri S. Kivshar,et al.  Nonlinear switching and solitons in PT‐symmetric photonic systems , 2015, 1509.03378.

[15]  Boris A. Malomed,et al.  Frontiers in multidimensional self-trapping of nonlinear fields and matter , 2019, Nature Reviews Physics.

[16]  Yasuhiro Ohta,et al.  General N‐Dark–Dark Solitons in the Coupled Nonlinear Schrödinger Equations , 2011 .

[17]  Jianke Yang,et al.  Rogue waves in the nonlocal $${\mathcal {PT}}$$PT-symmetric nonlinear Schrödinger equation , 2017, Letters in Mathematical Physics.

[18]  Liming Ling,et al.  Soliton solutions for the nonlocal nonlinear Schrödinger equation , 2016 .

[19]  Mark J. Ablowitz,et al.  General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions , 2017, Nonlinearity.

[20]  Yongshuai Zhang,et al.  Families of nonsingular soliton solutions of a nonlocal Schrödinger–Boussinesq equation , 2018, Nonlinear Dynamics.

[21]  M. Ablowitz,et al.  Integrable nonlocal nonlinear Schrödinger equation. , 2013, Physical review letters.

[22]  A. Khare,et al.  Periodic and hyperbolic soliton solutions of a number of nonlocal nonlinear equations , 2014, 1405.5267.

[23]  広田 良吾,et al.  The direct method in soliton theory , 2004 .

[24]  Yong Chen,et al.  Novel higher-order rational solitons and dynamics of the defocusing integrable nonlocal nonlinear Schrödinger equation via the determinants , 2017, Appl. Math. Lett..

[25]  Min Li,et al.  Dark and antidark soliton interactions in the nonlocal nonlinear Schrödinger equation with the self-induced parity-time-symmetric potential. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  M. Jimbo,et al.  Solitons and Infinite Dimensional Lie Algebras , 1983 .

[27]  Yong Chen,et al.  Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equations , 2018, Nonlinear Dynamics.

[28]  Shoufeng Shen,et al.  Solutions and connections of nonlocal derivative nonlinear Schrödinger equations , 2018, Nonlinear Dynamics.

[29]  Yong Chen,et al.  Reductions of Darboux transformations for the PT-symmetric nonlocal Davey-Stewartson equations , 2018, Appl. Math. Lett..

[30]  J. Rao,et al.  Rogue waves of the nonlocal Davey–Stewartson I equation , 2018, Nonlinearity.