Gardner equation

Gardner equation is a nonlinear partial differential equation set up by mathematician Clifford Gardner in 1968 to generalize KdV equation. Gardner equation has application in hydrodynamics, plasma physics and quantum field theory[1]


\frac{\partial u}{\partial t}+(2*a*u-3*b*u^2)*\frac{\partial u}{\partial x }+\frac{\partial^3 u}{\partial x^3}=0

Analytic solution

Gardner equation has traveling wave solutions[2]


 
 
 
 
 
 
 
 
 
 

Reference

  1. ↑ Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple p13 Springer
  2. ↑ Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple p201-202 Springer
  1. Graham W. Griffiths William E.Shiesser Traveling Wave Analysis of Partial Differential Equations Academy Press
  2. Richard H. Enns George C. McCGuire, Nonlinear Physics Birkhauser,1997
  3. Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple Springer.
  4. Eryk Infeld and George Rowlands,Nonlinear Waves,Solitons and Chaos,Cambridge 2000
  5. Saber Elaydi,An Introduction to Difference Equationns, Springer 2000
  6. Dongming Wang, Elimination Practice,Imperial College Press 2004
  7. David Betounes, Partial Differential Equations for Computational Science: With Maple and Vector Analysis Springer, 1998 ISBN 9780387983004
  8. George Articolo Partial Differential Equations & Boundary Value Problems with Maple V Academic Press 1998 ISBN 9780120644759