Explicit solutions to a nonlocal 2-component complex modified Korteweg-de Vries equation

Abstract A nonlocal 2-component complex modified Korteweg–de Vries equation will be investigated in this paper. We derive the N -fold Darboux transformation in the form of determinants. Based on the plane wave solutions, explicit solutions can be generated via this N -fold Darboux transformation. Moreover, dynamical behaviours of nonsingular solutions are discussed.

[1]  F. Tappert,et al.  Asymptotic Theory of Self-Trapping of Heat Pulses in Solids , 1970 .

[2]  Chengfa Wu,et al.  Rational solutions of the classical Boussinesq–Burgers system , 2018, Nonlinear Dynamics.

[3]  U. Peschel,et al.  Parity–time synthetic photonic lattices , 2012, Nature.

[4]  Guo-Fu Yu,et al.  Riemann-Hilbert approach and N-soliton formula for a higher-order Chen-Lee-Liu equation , 2018, Journal of Nonlinear Mathematical Physics.

[5]  A. Fokas,et al.  Generating mechanism for higher-order rogue waves. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  K. Chow,et al.  A coupled "AB" system: Rogue waves and modulation instabilities. , 2015, Chaos.

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

[8]  W. Liu,et al.  Dynamics of the smooth positons of the complex modified KdV equation , 2018 .

[9]  General soliton solutions to a coupled Fokas-Lenells equation , 2016, 1611.10057.

[10]  H. Erbay.  Nonlinear Transverse Waves in a Generalized Elastic Solid and the Complex Modified Korteweg–deVries Equation , 1998 .

[11]  Xujie Shi,et al.  Dynamics of soliton solutions of the nonlocal Kundu-nonlinear Schrödinger equation. , 2019, Chaos.

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

[13]  Liming Ling.  The algebraic representation for high order solution of Sasa-Satsuma equation , 2016 .

[14]  Asli Pekcan.  Nonlocal coupled HI-MKdv systems , 2019, Commun. Nonlinear Sci. Numer. Simul..

[15]  Exact Group Invariant Solutions and Conservation Laws of the Complex Modified Korteweg–de Vries Equation , 2013 .

[16]  E. Suhubi,et al.  Nonlinear wave propagation in micropolar media—I. The general theory , 1989 .

[17]  Dingyuan Tang,et al.  Recent progress of study on optical solitons in fiber lasers , 2019, Applied Physics Reviews.

[18]  R. Morandotti,et al.  Observation of PT-symmetry breaking in complex optical potentials. , 2009, Physical review letters.

[19]  Karen Uhlenbeck,et al.  Bäcklund transformations and loop group actions , 1998, math/9805074.

[20]  Jian Xu,et al.  The Riemann-Hilbert problem and long-time asymptotics for the Kundu-Eckhaus equation with decaying initial value , 2018, Appl. Math. Lett..

[21]  Komatsu,et al.  Kink soliton characterizing traffic congestion. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[22]  Jingsong He,et al.  Few-cycle optical rogue waves: complex modified Korteweg-de Vries equation. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  K. W. Chow,et al.  A system of coupled partial differential equations exhibiting both elevation and depression rogue wave modes , 2015, Appl. Math. Lett..

[24]  N. Zabusky.  A Synergetic Approach to Problems of Nonlinear Dispersive Wave Propagation and Interaction , 1967 .

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

[26]  M. Ablowitz,et al.  Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation , 2016 .

[27]  E. P. Zhidkov,et al.  Stability of a solution of the form of a solitary wave for a nonlinear complex modified Korteweg-de Vries equation , 1985 .

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

[29]  Charles F. F. Karney,et al.  Nonlinear evolution of lower hybrid waves , 1979 .

[30]  M. Ablowitz,et al.  Inverse Scattering Transform for the Nonlocal Reverse Space–Time Nonlinear Schrödinger Equation , 2018, Theoretical and Mathematical Physics.

[31]  Z. Musslimani,et al.  Beam dynamics in PT symmetric optical lattices. , 2008, Physical review letters.

[32]  Li-yuan Ma,et al.  Soliton solution and gauge equivalence for an integrable nonlocal complex modified Korteweg-de Vries equation , 2017 .