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In this work, we obtain some analytic solutions for the (3+1)-dimensional breaking soliton after obtaining its Hirota’s bilinear form. Our calculations show that, three-wave method is very easy and straightforward to solve nonlinear partial differential equations. Keywords—(3+1)-dimensional breaking soliton equation, Hirota’s bilinear form.
In this paper, the generalized (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (shortly CBS) equations are investigated. We employ the Hirota’s bilinear method to obtain the bilinear form of CBS equations. Then by the idea of extended homoclinic test approach (shortly EHTA), some exact soliton solutions including breather type solutions are presented.(More)
In this paper, using ( ′ G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.(More)
Approximated solutions to two-dimensional and axisymmetric jet impinging flows have been presented here. Assumptions have been made to reduce the related full Navier-Stokes equations to a non-linear ordinary differential equation. The Admomian decomposition method (ADM) has been employed to obtain an approximated solution to this differential equation. A(More)
By using the sine-cosine method proposed recently, we give the exact periodic and soliton solutions of the (2 + 1)-dimensional soliton equation in this paper. Many new families of exact traveling wave solutions of the (2 + 1)-dimensional soliton equation are successfully obtained. The computation for the method appears to be easier and faster by general(More)