Integrability, bilinearization, solitons and exact three wave solutions for a forced Korteweg-de Vries equation

[1]  Nikolai A. Kudryashov,et al.  Painleve analysis and exact solutions for the modified Korteweg-de Vries equation with polynomial source , 2016, Appl. Math. Comput..

[2]  Wen-Xiu Ma,et al.  EXACT ONE-PERIODIC AND TWO-PERIODIC WAVE SOLUTIONS TO HIROTA BILINEAR EQUATIONS IN (2+1) DIMENSIONS , 2008, 0812.4316.

[3]  Engui Fan,et al.  The integrability of nonisospectral and variable-coefficient KdV equation with binary Bell polynomials , 2011 .

[4]  S. A. El-Wakil,et al.  Self-similar solutions for some nonlinear evolution equations: KdV, mKdV and Burgers equations , 2016 .

[5]  M. Ali Akbar,et al.  Some new exact traveling wave solutions to the simplified MCH equation and the (1 + 1)-dimensional combined KdV–mKdV equations , 2015 .

[6]  Alvaro H. Salas,et al.  Computing solutions to a forced KdV equation , 2011 .

[7]  M. Wadati,et al.  Relationships among Inverse Method, Bäcklund Transformation and an Infinite Number of Conservation Laws , 1975 .

[8]  A. Wazwaz.  Painlevé analysis for Boiti–Leon–Manna–Pempinelli equation of higher dimensions with time-dependent coefficients: Multiple soliton solutions , 2020, Physics Letters A.

[9]  Zuntao Fu,et al.  JACOBI ELLIPTIC FUNCTION EXPANSION METHOD AND PERIODIC WAVE SOLUTIONS OF NONLINEAR WAVE EQUATIONS , 2001 .

[10]  M. Tabor,et al.  The Painlevé property for partial differential equations , 1983 .

[11]  Abdul-Majid Wazwaz,et al.  The tanh and the sine-cosine methods for the complex modified K dV and the generalized K dV equations , 2005 .

[12]  Sanjay Mishra,et al.  Nonlinear wave excitations by orbiting charged space debris objects , 2015 .

[13]  A. Seadawy,et al.  Painlevé analysis of a nonlinear Schrödinger equation discussing dynamics of solitons in optical fiber , 2020, International Journal of Modern Physics B.

[14]  Bo Tian,et al.  Solitons, Bäcklund transformation, and Lax pair for the "2 +1…-dimensional Boiti-Leon-Pempinelli equation for the water waves , 2010 .

[15]  Bo Tian,et al.  Solitons, Bäcklund transformation and Lax pair for a (2+1)-dimensional Davey-Stewartson system on surface waves of finite depth , 2018 .

[16]  Maria Luz Gandarias,et al.  Some conservation laws for a forced KdV equation , 2012 .

[17]  Wenxiu Ma,et al.  Bilinear Equations and Resonant Solutions Characterized by Bell Polynomials , 2013 .

[18]  Nikolai A. Kudryashov,et al.  Painlevé analysis and exact solutions of the Korteweg-de Vries equation with a source , 2015, Appl. Math. Lett..

[19]  Ryogo Hirota,et al.  Exact N‐soliton solutions of the wave equation of long waves in shallow‐water and in nonlinear lattices , 1973 .

[20]  Mingliang Wang,et al.  The (G' G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics , 2008 .

[21]  T. Miwa,et al.  Painlevé test for the self-dual Yang-Mills equation , 1982 .

[22]  Johan Springael,et al.  On a direct procedure for the disclosure of Lax pairs and Bäcklund transformations , 2001 .

[23]  Hengchun Hu,et al.  New interaction solutions to the combined KdV–mKdV equation from CTE method , 2016 .

[24]  Xing-Biao Hu,et al.  An integrable symmetric (2+1)-dimensional Lotka–Volterra equation and a family of its solutions , 2005 .

[25]  D. J. Benney.  Long Non‐Linear Waves in Fluid Flows , 1966 .

[26]  Ahmet Bekir.  Application of the (G′G)-expansion method for nonlinear evolution equations , 2008 .

[27]  Johan Springael,et al.  Soliton Equations and Simple Combinatorics , 2008 .

[28]  D. Korteweg,et al.  XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves , 1895 .

[29]  M. Tabor,et al.  Painlevé expansions for nonintegrable evolution equations , 1989 .

[30]  Chuanjian Wang,et al.  Lump solution and integrability for the associated Hirota bilinear equation , 2017 .

[31]  Wenxiu Ma,et al.  Lump solutions to the Kadomtsev–Petviashvili equation , 2015 .

[32]  P. Clarkson,et al.  Rational solutions of a differential-difference KdV equation, the Toda equation and the discrete KdV equation , 1995 .

[33]  R. Grimshaw,et al.  Resonantly generated internal waves in a contraction , 1994, Journal of Fluid Mechanics.

[34]  H. Washimi,et al.  ON THE PROPAGATION OF ION ACOUSTIC SOLITARY WAVES OF SMALL AMPLITUDE. , 1966 .

[35]  B. Duffy,et al.  An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations , 1996 .

[36]  Wen-Xiu Ma,et al.  Lump-type solutions to nonlinear differential equations derived from generalized bilinear equations , 2016 .

[37]  P. Chatterjee,et al.  Analytical electron acoustic solitary wave solution for the forced KdV equation in superthermal plasmas , 2017 .

[38]  Wenxiu Ma,et al.  Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions , 2004, nlin/0503001.

[39]  Zhengde Dai,et al.  Exact three-wave solutions for the (3+1)-dimensional Jimbo-Miwa equation , 2011, Comput. Math. Appl..

[40]  Guo Bo-ling,et al.  Analytic Solutions to Forced KdV Equation , 2009 .

[41]  J. Nimmo,et al.  On the combinatorics of the Hirota D-operators , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[42]  Wenxiu Ma.  N-soliton solutions and the Hirota conditions in (2+1)-dimensions , 2020 .

[43]  R. Grimshaw,et al.  Weakly nonlinear internal wave fronts trapped in contractions , 2000, Journal of Fluid Mechanics.

[44]  A. Wazwaz,et al.  Characteristics of integrability, bidirectional solitons and localized solutions for a ($$3+1$$3+1)-dimensional generalized breaking soliton equation , 2019, Nonlinear Dynamics.

[45]  Johan Springael,et al.  Construction of Bäcklund Transformations with Binary Bell Polynomials , 1997 .

[46]  Engui Fan,et al.  Super extension of Bell polynomials with applications to supersymmetric equations , 2012 .

[47]  Gui-Qiong Xu,et al.  Painlevé analysis, integrability and exact solutions for a (2 + 1)-dimensional generalized Nizhnik-Novikov-Veselov equation , 2016 .

[48]  Ji-Huan He.  Application of homotopy perturbation method to nonlinear wave equations , 2005 .

[49]  Zhanhui Zhao,et al.  Extend three-wave method for the (1+2)-dimensional Ito equation , 2010, Appl. Math. Comput..

[50]  Yong Chen,et al.  Bell polynomials approach for two higher-order KdV-type equations in fluids , 2016 .

[51]  Yehuda B. Band,et al.  Optical Solitary Waves in the Higher Order Nonlinear Schrödinger Equation , 1996, patt-sol/9612004.

[52]  A. Wazwaz,et al.  Integrability aspects and localized wave solutions for a new $$\mathbf (4+1) $$-dimensional Boiti–Leon–Manna–Pempinelli equation , 2019, Nonlinear Dynamics.

[53]  Lin Liang,et al.  Exact three-wave solution for higher dimensional KdV-type equation , 2010, Appl. Math. Comput..

[54]  Zhengde Dai,et al.  Exact three-wave solutions for the KP equation , 2010, Appl. Math. Comput..

[55]  Yi-Tian Gao,et al.  Painlevé analysis, Lie group analysis and soliton-cnoidal, resonant, hyperbolic function and rational solutions for the modified Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff equation in fluid mechanics/plasma physics , 2021 .