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Method for solving the Korteweg-deVries equation
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In this paper, a method for solving the initial value problem of the Korteweg-deVries equation is presented which is applicable to initial data that approach a constant sufficiently rapidly asAbstract:
A method for solving the initial-value problem of the Korteweg-deVries equation is presented which is applicable to initial data that approach a constant sufficiently rapidly as $|x|\ensuremath{\rightarrow}\ensuremath{\infty}$. The method can be used to predict exactly the "solitons," or solitary waves, which emerge from arbitrary initial conditions. Solutions that describe any finite number of solitons in interaction can be expressed in closed form.read more
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On a spectral transform of a KDV-like equation related to the Schrodinger operator in the plane
TL;DR: In this paper, a generalisation in 2+1 dimensions of the Korteweg-de Vries (KDV) equation is related to the Schrodinger operator in the plane.
Journal ArticleDOI
Optical solitons and quasisolitons
TL;DR: In this paper, it was shown that both solitons and quasisolitons can exist, if the linear operator specifying their asymptotic behavior at infinity is sign-definite.
Journal ArticleDOI
On modified method of simplest equation for obtaining exact and approximate solutions of nonlinear PDEs: The role of the simplest equation
TL;DR: The modified method of simplest equation is powerful tool for obtaining exact and approximate solutions of nonlinear PDEs as discussed by the authors, which are constructed on the basis of solutions of more simple equations called simplest equations.
Journal ArticleDOI
The reductive perturbation method and some of its applications
TL;DR: The reductive perturbation method is a very powerful way of deriving simplified models describing nonlinear wave propagation and interaction as mentioned in this paper, and it has been applied in many applications, such as ultrafast or wave propagation in ferromagnetic media.
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