Resonant collisions among multi-breathers in the Mel’nikov system

[1]  J. Rao,et al.  Degenerate and non-degenerate vector solitons and their interactions in the two-component long-wave–short-wave model of Newell type , 2023, Chaos, Solitons & Fractals.

[2]  B. Malomed Multidimensional dissipative solitons and solitary vortices , 2022, Chaos, Solitons & Fractals.

[3]  J. Rao,et al.  A study on resonant collision in the two-dimensional multi-component long-wave–short-wave resonance system , 2022, Proceedings of the Royal Society A.

[4]  Jingsong He,et al.  Resonant collisions among two-dimensional localized waves in the Mel’nikov equation , 2021, Nonlinear Dynamics.

[5]  Ai-Hua Chen,et al.  Dynamic properties of interactional solutions for the (4 + 1)-dimensional Fokas equation , 2021, Nonlinear Dynamics.

[6]  Wei Liu,et al.  Two-dimensional new coherent structures of lump-soliton solutions for the Mel’nikov equation , 2021, Modern Physics Letters B.

[7]  V. Zakharov,et al.  Lump chains in the KP‐I equation , 2021, Studies in Applied Mathematics.

[8]  Jiguang Rao,et al.  Dynamics of interaction between lumps and solitons in the Mel'nikov equation , 2020, Commun. Nonlinear Sci. Numer. Simul..

[9]  Ai-Hua Chen,et al.  Resonant solitary wave and resonant periodic wave solutions of the Kudryashov-Sinelshchikov equation , 2020, Physica Scripta.

[10]  Ji Lin,et al.  Lump and Mixed Rogue-Soliton Solutions of the (2 + 1)-Dimensional Mel'nikov System , 2019, Complex..

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

[12]  Yong Chen,et al.  Hybrid solutions to Mel’nikov system , 2018, Nonlinear Dynamics.

[13]  Junchao Chen,et al.  The Derivative Yajima–Oikawa System: Bright, Dark Soliton and Breather Solutions , 2018 .

[14]  A. Wazwaz,et al.  Interaction of lumps and dark solitons in the Mel’nikov equation , 2018 .

[15]  Yong Chen,et al.  General bright–dark soliton solution to (2 + 1)-dimensional multi-component long-wave–short-wave resonance interaction system , 2017 .

[16]  Bao-Feng Feng,et al.  General Mixed Multi-Soliton Solutions to One-Dimensional Multicomponent Yajima-Oikawa System , 2015, 1506.04932.

[17]  M. Lakshmanan,et al.  Dynamics of solitons in multicomponent long wave–short wave resonance interaction system , 2015, 1512.01034.

[18]  M Lakshmanan,et al.  Multicomponent long-wave-short-wave resonance interaction system: Bright solitons, energy-sharing collisions, and resonant solitons. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Zhenyun Qin,et al.  Two spatial dimensional N-rogue waves and their dynamics in Mel’nikov equation , 2014 .

[20]  S. Winnerl,et al.  Optical excitation of Josephson plasma solitons in a cuprate superconductor. , 2013, Nature materials.

[21]  M Lakshmanan,et al.  Mixed solitons in a (2+1)-dimensional multicomponent long-wave-short-wave system. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  M. Ablowitz,et al.  Nonlinear shallow ocean-wave soliton interactions on flat beaches. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Adrian Ankiewicz,et al.  Dissipative soliton resonances in the anomalous dispersion regime , 2009 .

[24]  M. Lakshmanan,et al.  Higher dimensional bright solitons and their collisions in a multicomponent long wave–short wave system , 2008, 0810.2868.

[25]  Adrian Ankiewicz,et al.  Dissipative soliton resonances , 2008 .

[26]  W. M. Liu,et al.  Controlling soliton interactions in Bose-Einstein condensates by synchronizing the Feshbach resonance and harmonic trap , 2008, 0808.3831.

[27]  H. Ruan,et al.  Interactions between the y-periodic solution and the algebraic solution of the (2+1)-dimensional Sawada–Kotera equation , 2006 .

[28]  C. Kumar,et al.  Exponentially localized solutions of Mel'nikov equation , 2004, nlin/0403044.

[29]  M. Tajiri,et al.  Note on Periodic Soliton Resonance: Solutions to the Davey-Stewartson II Equation : General Physics , 2001 .

[30]  Yosuke Watanabe,et al.  Periodic soliton resonance : Solutions to the Davey-Stewartson I equation , 1998 .

[31]  Pietsch,et al.  Nonlinear mode conversion with chaotic soliton generation at plasma resonance. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  Y. Murakami,et al.  Interactions between two y-periodic solitons: solutions to the Kadomtsev-Petviashvili equation with positive dispersion , 1991 .

[33]  Youichi Murakami,et al.  Two-Dimensional Multisoliton Solutions: Periodic Soliton Solutions to the Kadomtsev-Petviashvili Equation with Positive Dispersion , 1989 .

[34]  Yoko Hase,et al.  Soliton Solutions to the Mel'nikov Equations , 1989 .

[35]  V. K. Mel’nikov A direct method for deriving a multi-soliton solution for the problem of interaction of waves on thex,y plane , 1987 .

[36]  V. Melnikov Reflection of waves in nonlinear integrable systems , 1987 .

[37]  V. K. Mel’nikov Wave emission and absorption in a nonlinear integrable system , 1986 .

[38]  V. K. Mel’nikov On equations for wave interactions , 1983 .

[39]  John W. Miles,et al.  Resonantly interacting solitary waves , 1977, Journal of Fluid Mechanics.

[40]  C. S. Gardner,et al.  Method for solving the Korteweg-deVries equation , 1967 .

[41]  B. Malomed,et al.  NONLINEAR WAVES IN OPTICAL AND MATTER-WAVE MEDIA : A TOPICAL SURVEY OF RECENT THEORETICAL AND EXPERIMENTAL RESULTS , 2019 .

[42]  A. Zaitsev Formation of stationary nonlinear waves by superposition of solitons , 1984 .

[43]  N. C. Freeman,et al.  Soliton Interactions in Two Dimensions , 1980 .

[44]  Alan C. Newell,et al.  Breakdown of Zakharov-Shabat theory and soliton creation , 1977 .