Articles | Volume 11, issue 3
https://doi.org/10.5194/nhess-11-667-2011
© Author(s) 2011. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/nhess-11-667-2011
© Author(s) 2011. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Multi-rogue waves solutions to the focusing NLS equation and the KP-I equation
P. Dubard
IMB, Université de Bourgogne, 9 av. Alain Savary, Dijon, France
V. B. Matveev
IMB, Université de Bourgogne, 9 av. Alain Savary, Dijon, France
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- General Rogue Waves in the Boussinesq Equation B. Yang & J. Yang
- High-order rogue waves for the Hirota equation L. Li et al.
- Dynamics of transformed nonlinear waves in the (3+1)-dimensional B-type Kadomtsev–Petviashvili equation I: Transitions mechanisms X. Zhang et al.
- Решение нелинейного уравнения Шредингера в виде двухфазных странных волн А. Смирнов & A. Smirnov
- Higher-Order Rogue Wave Solutions to a Spatial Discrete Hirota Equation J. Yang & Z. Zhu
- Freak Waves as a Result of Modulation Instability V. Zakharov & A. Gelash
- Multi-lump solutions of KPI S. Chakravarty
- Generating mechanism for higher-order rogue waves J. He et al.
- Asymptotic Analysis of Multilump Solutions of the Kadomtsev–Petviashvili-I Equation J. Chang
- Persistence of rogue waves in extended nonlinear Schrödinger equations: Integrable Sasa–Satsuma case U. Bandelow & N. Akhmediev
- Dynamics of rogue waves on multisoliton background in the Benjamin Ono equation Y. LIU & B. LI
- Constructing rogue wave prototypes of nonlinear evolution equations via an extended tanh method Z. Lü & Y. Chen
- AKNS and NLS hierarchies, MRW solutions, P n breathers, and beyond V. Matveev & A. Smirnov
- Rogue Waves and Hybrid Solutions of the Boussinesq Equation J. Rao et al.
- Преобразование Дарбу для системы Вадати - Коно - Итикавы Ю. Чжан et al.
- N-order bright and dark rogue waves in a resonant erbium-doped fiber system J. He et al.
- Dynamics of KPI lumps S. Chakravarty & M. Zowada
- Novel high‐order breathers and rogue waves in the Boussinesq equation via determinants Y. Liu et al.
- Two-dimensional self-similarity transformation theory and line rogue waves excitation J. Zhang et al.
- General rogue wave solution to the discrete nonlinear Schrödinger equation Y. Ohta & B. Feng
- Darboux transformation and Rogue waves of the Kundu-nonlinear Schrödinger equation C. Zhang et al.
- Dynamic behaviors of bright and dark rogue waves for the (2+1) dimensional Nizhnik–Novikov–Veselov equation C. Wang & Z. Dai
- Circular viewpoint of higher-order rogue wave structures of the nonlinear Schrödinger equation A. Ankiewicz
- Complex nonlinearities of rogue waves in generalized inhomogeneous higher-order nonlinear Schrödinger equation N. Song et al.
- Dynamics of higher-order rational solitons for the nonlocal nonlinear Schrödinger equation with the self-induced parity-time-symmetric potential X. Wen et al.
- The phase patterns of higher-order rogue waves D. Kedziora et al.
- Circular rogue wave clusters D. Kedziora et al.
- Rational solutions of the Boussinesq equation and applications to rogue waves P. Clarkson & E. Dowie
- Solutions of the Ablowitz–Kaup–Newell–Segur hierarchy equations of the “rogue wave” type: A unified approach V. Matveev & A. Smirnov
- Rogue waves, rational solitons and wave turbulence theory B. Kibler et al.
- Numerical study on the generation and evolution of the super-rogue waves J. Yang & W. Lu
- Novel nonlinear wave equation: Regulated rogue waves and accelerated soliton solutions A. Mukherjee & A. Kundu
- Kadomtsev–Petviashvili equation: One-constraint method and lump pattern J. Dong et al.
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- General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation Y. Ohta & J. Yang
- High‐Order Solutions and Generalized Darboux Transformations of Derivative Nonlinear Schrödinger Equations B. Guo et al.
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- Few-cycle optical rogue waves: Complex modified Korteweg–de Vries equation J. He et al.
- Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents A. Kundu et al.
- Breathers-like rogue wave trains induced by nonlinear dynamics of DNA breathing B. Essama et al.
- N-fold Darboux transformation of the two-component Kundu–Eckhaus equations and non-symmetric doubly localized rogue waves D. Qiu & W. Cheng
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- Interactions of localized wave and dynamics analysis in generalized derivative nonlinear Schrödinger equation X. Li et al.
- Rogue waves in the basin of intermediate depth and the possibility of their formation due to the modulational instability I. Didenkulova et al.
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- A novel investigation of dark, bright, and periodic soliton solutions for the Kadomtsev-Petviashvili equation via different techniques A. Butt et al.
- General breather and rogue wave solutions to the complex short pulse equation B. Feng et al.
- Generalized Darboux transformation and rogue wave solutions for the higher-order dispersive nonlinear Schrödinger equation B. Yang et al.
- Modulational instability and dynamics of implicit higher-order rogue wave solutions for the Kundu equation X. Wen & G. Zhang
- Line Rogue Waves in the Mel’nikov Equation Y. Shi
- Rational and semi-rational solutions of the Kadomtsev–Petviashvili-based system Y. Zhang et al.
- Периодические двухфазные “волны-убийцы” А. Смирнов & A. Smirnov
- Волны-убийцы в бароклинных течениях Д. Цзо et al.
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- Modulational instability and higher order-rogue wave solutions for the generalized discrete Hirota equation X. Wen & D. Wang
- Solitons to rogue waves transition, lump solutions and interaction solutions for the (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation in fluid dynamics X. Yan et al.
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- Nonlinear Schrödinger equation: Generalized Darboux transformation and rogue wave solutions B. Guo et al.
- Higher-order rogue wave solutions to the Kadomtsev–Petviashvili 1 equation L. Guo et al.
- Numerical spectral synthesis of breather gas for the focusing nonlinear Schrödinger equation G. Roberti et al.
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- Breathers, rogue waves, and interaction solutions for the variable coefficient Kundu-nonlinear Schrödinger equation X. Zhang et al.
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- Two spatial dimensional N-rogue waves and their dynamics in Mel’nikov equation G. Mu & Z. Qin
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- Recent progress in investigating optical rogue waves N. Akhmediev et al.
- General High-order Rogue Waves of the (1+1)-Dimensional Yajima–Oikawa System J. Chen et al.
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- Families of quasi-rational solutions of the NLS equation and multi-rogue waves P. Gaillard
- Multi-rogue waves solutions: from the NLS to the KP-I equation P. Dubard & V. Matveev
- Instabilities, breathers and rogue waves in optics J. Dudley et al.
- Conservation Laws and Integral Relations for the Boussinesq Equation A. Ankiewicz et al.
- Lump and rogue wave solutions to a (2+1)-dimensional Boussinesq type equation Y. Zhou et al.
- Then-order rogue waves of Fokas-Lenells equation S. Xu et al.
- On general rogue waves in the parity-time-symmetric nonlinear Schrödinger equation B. Yang & J. Yang
- Families of exact solutions of a new extended $$\varvec{(2+1)}$$(2+1)-dimensional Boussinesq equation Y. Cao et al.
- Dispersive shock wave, generalized Laguerre polynomials, and asymptotic solitons of the focusing nonlinear Schrödinger equation V. Kotlyarov & A. Minakov
- Nonlocal Solitons in a Nonlinear Chain of Atoms T. Gadzhimuradov & A. Agalarov
- Rogue-wave solutions of the Zakharov equation J. Rao et al.
- Rogue waves in the nonlocal $${\mathcal {PT}}$$ PT -symmetric nonlinear Schrödinger equation B. Yang & J. Yang
- Rogue waves and hybrid solutions of the Davey–Stewartson I equation Y. Liu et al.
- The Darboux transformation for the Wadati–Konno–Ichikawa system Y. Zhang et al.
- Triangular rogue wave cascades D. Kedziora et al.
- Hybrid structures of the rogue waves and breather-like waves for the higher-order coupled nonlinear Schrödinger equations X. Zhang et al.
- Coupled cubic-quintic nonlinear Schrödinger equation: novel bright–dark rogue waves and dynamics X. Yan & J. Zhang
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- Semi-rational solutions of the third-type Davey-Stewartson equation J. Rao et al.
- Novel curved lump and topological solitons of integrable (2+1) dimensional KMN equation A. Mukherjee
- Spatial Self-Similar Transformation and Novel Line Rogue Waves of the Fokas System J. Zhang & M. Jin
- Periodic line wave, rogue waves and the interaction solutions of the (2+1)-dimensional integrable Kadomtsev–Petviashvili-based system Y. Liu & Z. Zhao
- Rogue Waves in the Three-Dimensional Kadomtsev—Petviashvili Equation C. Qian et al.
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- Role of Homoclinic Breathers in the Interpretation of Experimental Measurements, With Emphasis on the Peregrine Breather A. Osborne
- From generalized Fourier transforms to spectral curves for the Manakov hierarchy. I. Generalized Fourier transforms V. Gerdjikov et al.
- Periodic-background solutions of Kadomtsev-Petviashvili I equation R. Li & X. Geng
- Rational solutions to two- and one-dimensional multicomponent Yajima–Oikawa systems J. Chen et al.
- Rational, semi-rational solution and self-consistent sources extension of the variable-coefficient extended modified Kadomtsev-Petviashvili equation R. Hai & H. Gegen
- Riemann–Hilbert Approach and Multiple Arbitrary-Order Pole Solutions for the Lakshmanan–Porsezian–Daniel Equation with Finite Density Initial Data W. Zhou & S. Tian
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- Dynamics of Nth-order rogue waves in ( $$2+1$$ 2 + 1 )-dimensional Hirota equation H. Gao
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- General high–order breathers and rogue waves in the(3+1)-dimensional KP–Boussinesq equation B. Sun & A. Wazwaz
- Rogue waves of the Sasa-Satsuma equation in a chaotic wave field J. Soto-Crespo et al.
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- On the Question of the Bäcklund Transformations and Jordan Generalizations of the Second Painlevé Equation A. Yurov & V. Yurov
- Construction of rational solutions of the real modified Korteweg-de Vries equation from its periodic solutions Q. Xing et al.
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- State transition induced by higher-order effects and background frequency C. Liu et al.
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