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M. Arshad, A. Seadawy, D. Lu (2017)
Exact bright-dark solitary wave solutions of the higher-order cubic-quintic nonlinear Schrödinger equation and its stabilityOptik, 138
Dipankar Kumar, A. Seadawy, A. Joardar (2018)
Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biologyChinese Journal of Physics, 56
M. Ablowitz, D. Kaup, A. Newell, H. Segur (1974)
The Inverse scattering transform fourier analysis for nonlinear problemsStudies in Applied Mathematics, 53
Hailing Lü, Xi-qiang Liu, Na Liu (2010)
Explicit solutions of the (2 + 1)-dimensional AKNS shallow water wave equation with variable coefficientsAppl. Math. Comput., 217
M. Ablowitz, D. Kaup, A. Newell, H. Segur (1973)
Nonlinear-evolution equations of physical significancePhysical Review Letters, 31
A. Khater, D. Callebaut, M. Helal, A. Seadawy (2006)
Variational method for the nonlinear dynamics of an elliptic magnetic stagnation lineThe European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics, 39
(2017)
Bistable Bright-Dark Solitary Wave Solutions of the (3+1)-Dimensional Breaking Soliton, Boussinesq Equation with Dual Dispersion andModified KdV-KP equations and their applications
K. Tariq, A. Seadawy (2017)
Bistable Bright-Dark solitary wave solutions of the (3 + 1)-dimensional Breaking soliton, Boussinesq equation with dual dispersion and modified Korteweg–de Vries–Kadomtsev–Petviashvili equations and their applicationsResults in physics, 7
M. Khater, A. Seadawy, D. Lu (2017)
Elliptic and solitary wave solutions for Bogoyavlenskii equations system, couple Boiti-Leon-Pempinelli equations system and Time-fractional Cahn-Allen equationResults in physics, 7
Shen Shou-feng (2006)
General multi-linear variable separation approach to solving low dimensional nonlinear systems and localized exitations, 55
V. Zakharov, A. Shabat (1970)
Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear MediaJournal of Experimental and Theoretical Physics, 34
M. Helal, A. Seadawy, S. Arabia (2013)
Stability Analysis Solutions for the Fourth-Order Nonlinear Ablowitz-Kaup-Newell-Segur Water Wave EquationApplied mathematical sciences, 7
(2015)
Exact solutionsof thegeneralized ( 2 + 1 ) - dimensional nonlinear evolution equations via the modified simple
Mohammed Al-Amr (2015)
Exact solutions of the generalized (2+1)-dimensional nonlinear evolution equations via the modified simple equation methodComput. Math. Appl., 69
A. Seadawy (2012)
The Solutions of the Boussinesq and Generalized Fifth-Order KdV Equations by Using the Direct Algebraic Method
A. Seadawy, D. Lu, M. Khater (2017)
Bifurcations of traveling wave solutions for Dodd–Bullough–Mikhailov equation and coupled Higgs equation and their applicationsChinese Journal of Physics, 55
D. Lu, A. Seadawy, M. Khater (2017)
Bifurcations of new multi soliton solutions of the van der Waals normal form for fluidized granular matter via six different methodsResults in physics, 7
A. Seadawy (2017)
Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water wavesThe European Physical Journal Plus, 132
JETP, 34
S. Tripathy, B. Mishra, P. Sahoo (2015)
Two fluid anisotropic dark energy models in a scale invariant theoryThe European Physical Journal Plus, 132
V. Matveev, A. Smirnov (2016)
Theoretical and Mathematical Physics, 186(2): 156–182 (2016) SOLUTIONS OF THE ABLOWITZ–KAUP–NEWELL–SEGUR HIERARCHY EQUATIONS OF THE “ROGUE WAVE” TYPE: A UNIFIED APPROACH
A. Seadawy (2012)
Exact solutions of a two-dimensional nonlinear Schrödinger equationAppl. Math. Lett., 25
(1991)
Darboux Transformation and Solitons
A. Seadawy (2015)
Nonlinear wave solutions of the three-dimensional Zakharov–Kuznetsov–Burgers equation in dusty plasmaPhysica A-statistical Mechanics and Its Applications, 439
Yi Zhang, Dengyuan Chen (2004)
Bäcklund transformation and soliton solutions for the shallow water waves equationChaos Solitons & Fractals, 20
Y. Shang (2007)
Bäcklund transformation, Lax pairs and explicit exact solutions for the shallow water waves equationAppl. Math. Comput., 187
(1974)
A scheme for integrating the nonlinear equations ofmathematical physics by themethod of inverse scattering transform
M. Helal, A. Seadawy (2011)
Exact soliton solutions of a D-dimensional nonlinear Schrödinger equation with damping and diffusive termsZeitschrift für angewandte Mathematik und Physik, 62
D. Lu, A. Seadawy, M. Arshad (2017)
Applications of extended simple equation method on unstable nonlinear Schrödinger equationsOptik, 140
(2012)
Traveling wave solutions of the Boussinesq and generalized fifth-order KdV equations by using the direct algebraic method
A. Khater, D. Callebaut, A. Seadawy (2000)
General Soliton Solutions of an n-Dimensional Complex Ginzburg–Landau EquationPhysica Scripta, 62
(2007)
transformation, Lax pairs and explicit exact solutions for the shallowwater waves
A. Seadawy (2016)
Stability Analysis of Traveling Wave Solutions for Generalized Coupled Nonlinear KdV EquationsApplied Mathematics & Information Sciences, 10
V. Matveev, M. Salle (1992)
Darboux Transformations and Solitons
AbstractThe aim of this article is to construct some new traveling wave solutions and investigate localized structures for fourth-order nonlinear Ablowitz-Kaup-Newell-Segur (AKNS) water wave dynamical equation. The simple equation method (SEM) and the modified simple equation method (MSEM) are applied in this paper to construct the analytical traveling wave solutions of AKNS equation. The different waves solutions are derived by assigning special values to the parameters. The obtained results have their importance in the field of physics and other areas of applied sciences. All the solutions are also graphically represented. The constructed results are often helpful for studying several new localized structures and the waves interaction in the high-dimensional models.
Open Physics – de Gruyter
Published: May 24, 2018
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