Solving Quasi-linear PDEs: The Gordon Sine Equation

Quasi-linear equation are those that have coefficients that depend on the unknown function. This is the case of the Gordon's sine equation: U_xx-U_tt=sin(U).
This equation arises in condensed material phenomenon. Some of the solutions of this equation are solitons, that are waves that propagate without dissipation and after collide with others, they don't destroy nor deform.
The next applet shows the solution of this equation.

Theory pages:
Main page	FEM (i)	FEM (ii)	FDM (i)

Example pages:
1-d Heat Equation	2-d steady state Heat Equation
2-d Heat Equation	1-d non diffusive transport equation
1-d diffusive transport equation	2-d Non diffusive transport equation
Mesh generation with OOCSMP	Moving grids

Application pages:
Heating of two beams	Heating of two moving beams
Solving the equation U_t+U_xx+U_xy+U_yx=0	Solving the equation U_t+U_xx+U_xy+U_yx=0 using MGEN
Heat 1d using several outputs	Solving the Heat equation with a CA
Comparing a CA with the FEM	Gordon's sine equation

Other courses
Gravitation	Ecology	Electronics	PDEs	Other pages

Last modified 2/1/2000 by Juan de Lara ( Juan.Lara@ii.uam.es, http://www.ii.uam.es/~jlara) need help for using this courses?.

The OOCSMP code - The SODA code