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This paper considers the generalized KdV equation with or without natural boundary conditions and provides a parameter region for solitons and solitary waves, and also modifies a result of Zabusky's.
      
The exact solutions and solitary solutions of NLPDE are obtained.
      
With modulus m → 1 or m → 0, these solutions degenerate into corresponding solitary wave solutions, shock wave solutions and trigonometric function solutions.
      
As is well known, Korteweg-de Vries equation is a typical one which has planar solitary wave.
      
By considering higher order transverse disturbance to planar solitary waves, we study a Kadomtsev-Petviashvili (KP) equation and find some interesting results.
      
Solitary wave solutions of nonlinear financial markets: data-modeling-concept-practicing
      
The gland is most developed in solitary species (Arctic, red, and corsac foxes) where it is represented by powerful glandular layer with large secretion containers-cisterns.
      
One-dimensional MHD simulations of solitary sharp and strong disturbances (impulses) of the interplanetary magnetic field and plasma of the homogeneous solar wind were performed.
      
The VDIS represent solitary structures of 0.3-10 keV consisting of several small-scale structures 2-5 min long, while the TDIS are repeating injections of 1-14 keV 1-3 min long with the repetition period of 2-4 min.
      
Behavior of perturbations of solitary and periodic waves on the surface of a heavy liquid
      
A solitary wave is a particular case of a wave train in which the length of the waves in the train is large.
      
In [2, 3] a quasilinear system of partial differential equations was obtained which described two-dimensional and three-dimensional motion of a solitary wave in a layer of liquid of variable depth.
      
We make our presentation for the solitary wave case; however, in view of our statement above, the results automatically carry over to the case of a train of waves.
      
Movement of solitary and periodic waves with an amplitude close to the limiting in a liquid layer of slowly varying depth
      
Solitary waves in a thin layer of viscous liquid which is running down a vertical surface under the action of gravity are investigated.
      
It is shown that in each case a solution of solitary wave type exists along with the single-parameter family of periodic solutions (parameter-the wave number α).
      
On decreasing the wave number, the periodic waves go over into a succession of solitary waves.
      
A study is made of the influence of an underwater ridge on a solitary wave that prior to the interaction with the ridge has the form of a circle situated outside the ridge.
      
It is shown that a solitary wave exists for discrete values of the dimensionless parameter.
      
The well-known solutions of this equation in the form of a solitary wave and a cnoidal wave are considered.
      
 

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