Approximate Analytical and Numeric Solutions to a Forced Damped Gardner Equation
Open Access
- 11 May 2022
- journal article
- research article
- Published by Hindawi Limited in The Scientific World Journal
- Vol. 2022, 1-10
- https://doi.org/10.1155/2022/3240918
Abstract
In this paper, some exact traveling wave solutions to the integrable Gardner equation are reported. The ansatz method is devoted for deriving some exact solutions in terms of Jacobi and Weierstrass elliptic functions. The obtained analytic solutions recover the solitary waves, shock waves, and cnoidal waves. Also, the relation between the Jacobi and Weierstrass elliptic functions is obtained. In the second part of this work, we derive some approximate analytic and numeric solutions to the nonintegrable forced damped Gardner equation. For the approximate analytic solutions, the ansatz method is considered. With respect to the numerical solutions, the evolution equation is solved using both the finite different method (FDM) and cubic B-splines method. A comparison between different approximations is reported.Keywords
This publication has 34 references indexed in Scilit:
- Nonlinear electrostatic excitations in electron-depleted electronegative dusty plasma with two-negative ion speciesAstrophysics and Space Science, 2011
- Semiclassical solitons in strongly correlated systems of ultracold bosonic atoms in optical latticesAnnals of Physics, 2011
- Plasma with two-negative ions and immobile dust particles: planar and non-planar ion-acoustic wave propagationThe European Physical Journal D, 2011
- Rogue internal waves in the ocean: Long wave modelThe European Physical Journal Special Topics, 2010
- Freak waves in laboratory and space plasmasThe European Physical Journal Special Topics, 2010
- On traveling wave solutions to combined KdV–mKdV equation and modified Burgers–KdV equationCommunications in Nonlinear Science and Numerical Simulation, 2009
- Dynamics of modulationally unstable ion-acoustic wavepackets in plasmas with negative ionsJournal of Plasma Physics, 2008
- New kinds of solutions to Gardner equationChaos, Solitons, and Fractals, 2004
- Soliton Perturbations for a Combined KdV-MKdV EquationChinese Physics Letters, 2000
- A super Korteweg-de Vries equation: An integrable systemPhysics Letters A, 1984