Sine-Gordon equation: Difference between revisions
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The '''sine-Gordon equation''' | The '''sine-Gordon equation''' | ||
<center><math>\Box u = sin(u)</math></center> | <center><math>\Box u = \sin(u)</math></center> | ||
in <math>R^{1+1}</math> arises in the study of optical pulses, or from the Scott model of a continuum of pendula hanging from a wire. It is a [[completely integrable]] equation, and has many interesting solutions, including "breather" solutions. | in <math>R^{1+1}</math> arises in the study of optical pulses, or from the Scott model of a continuum of pendula hanging from a wire. It is a [[completely integrable]] equation, and has many interesting solutions, including "breather" solutions. | ||
Because the non-linearity is bounded, GWP is easily obtained for <math>L^2</math> or even <math>L^1</math> data. | Because the non-linearity is bounded, GWP is easily obtained for <math>L^2</math> or even <math>L^1</math> data. | ||
It is also closely related to the '''sinh-Gordon equation''' | |||
<center><math>\Box u = \sinh(u)</math></center> | |||
and to [[Liouville's equation]]. | |||
[[Category:Integrability]] | [[Category:Integrability]] | ||
[[Category:wave]] | [[Category:wave]] | ||
[[Category:Equations]] | [[Category:Equations]] | ||
Latest revision as of 23:39, 22 January 2009
[Contributions to this section are sorely needed!]
The sine-Gordon equation
in arises in the study of optical pulses, or from the Scott model of a continuum of pendula hanging from a wire. It is a completely integrable equation, and has many interesting solutions, including "breather" solutions.
Because the non-linearity is bounded, GWP is easily obtained for or even data.
It is also closely related to the sinh-Gordon equation
and to Liouville's equation.
