We explain how to apply techniques from integrable systems to construct 2k-soliton homoclinic wave maps from the periodic Minkowski space S ×R to a compact Lie group, and more generally to a compact symmetric space. We give a correspondence between solutions of the −1 flow equation associated to a compact Lie group G and wave maps into G. We use Bäcklund transformations to construct explicit 2k...

In this article, we apply the improved (G′/G)-expansion method to construct some new exact traveling wave solutions including soliton and periodic solutions of the combined KdV-MKdV equation involving parameters. In this method, G′′+λG′+μG = 0 together with ( ) ( ) j m

Abstract: This manuscript focuses attention on new exact solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave. The extended trial equation method (ETEM), which is one of the analytical methods, has been handled for finding exact solutions of the system of equations for the ion sound wave and...

Abstract. Bright plane soliton solutions of an integrable (2+1) dimensional (n+1)wave system are obtained by applying Hirota’s bilinearization method. First, the soliton solutions of a 3-wave system consisting of two short wave components and one long wave component are found and then the results are generalized to the corresponding integrable (n+1)-wave system with n short waves and single lon...

In this work, we established exact solutions for some nonlinear evolution equations. The tanhcoth method was used to construct solitary and soliton solutions of (2+1)-dimensional nonlinear evolution equations. The tanh-coth method presents a wider applicability for handling nonlinear wave equations.

By using the sine-cosine method proposed recently, we give the exact periodic and soliton solutions of the (2 + 1)-dimensional Bogoyavlenskii equation in this paper. Many new families of exact traveling wave solutions of the (2 + 1)-dimensional Bogoyavlenskii equation are successfully obtained. The computation for the method appears to be easier and faster by general mathematical software.

We derive the properties of self-induced transparency ~SIT! solitary waves in a one-dimensional periodic structure doped uniformly with resonance two-level atoms. In our model, the electromagnetic field is treated classically and the dopant atoms are described quantum mechanically. The resulting solitary waves take the form of ultrashort ~picosecond! laser pulses which propagate near the band e...

The exact solutions of the wave equation for arbitrary spin particles in the field of the soliton-like electric impulse were obtained. The differential probability of pair production of particles by electromagnetic fields has been evaluated on the basis of the exact solutions. As a particular case, the particle pair producing in the constant and uniform electric field were studied.

The KP hierarchy reduction method is one of the most reliable and efficient techniques for determining exact solitary wave solutions to nonlinear partial differential equations. In this paper, according technique, rational some other semi-rational (2 + 1)-dimensional Maccari system are investigated. It shown that two different types breathers can be derived, under appropriate parameter constrai...

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