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Solitons pp 157-176 | Cite as

Direct Methods in Soliton Theory

  • R. Hirota
Part of the Topics in Current Physics book series (TCPHY, volume 17)

Abstract

The main purpos e of this chapter is to present a direct and systematic way of finding exact solutions and Bäcklund transformations of a certain class of nonlinear evolution equations. The nonlinear evolution equations are transformed, by changing the dependent variable(s), into bilinear differential equations of the following special form
$$ F\left( {\frac{\partial }{{\partial t}} - \frac{\partial }{{\partial {t^1}}},\frac{\partial }{{\partial x}} - \frac{\partial }{{\partial {x^1}}}} \right)f(t,x)f({t^1},{x^1}){|_{t = {t^1},x = {x^1}}} = 0 $$
, which we solve exactly using a kind of perturbational approach.

Keywords

Bilinear Form Nonlinear Evolution Equation Boussinesq Equation Toda Equation Power Series Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1980

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  • R. Hirota

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