By applying a special Bäcklund transformation, a general variable separation solution for the (2+1)-dimensional higher-order Broer-Kaup system is derived. In addition to some types of the usual localized excitations, such as dromions, lumps, ring solitons, oscillated dromions and breathers, soliton structures can be easily constructed by selecting arbitrary functions appropriately. A new class ...

In this paper, the tanh and sine–cosine methods are used to construct exact periodic and soliton solutions of nonlinear evolution equations arising in mathematical physics. Many new families of exact travelling wave solutions of the generalized Hirota–Satsuma coupled KdV system, generalized-Zakharov equations and (2 + 1)-dimensional Broer–Kaup– Kupershmidt system are successfully obtained. The ...

In this paper, based on the fractional Riccati equation, we propose an extended fractional Riccati sub-equation method for solving fractional partial differential equations. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By a proposed variable transformation, certain fractional partial differential equations are turned into fractional ordinary di...

Complex systems (CS) are pervasive in many areas, namely financial markets; highway transportation; telecommunication networks; world and country economies; social networks; immunological systems; living organisms; computational systems; and electrical and mechanical structures. CS are often composed of a large number of interconnected and interacting entities exhibiting much richer global scal...

Many methods have been developed by scientists to find solutions for nonlinear problems. In this paper, the general structure of modified trial equation method (MTEM) is introduced, and MTEM used some exact (2+1)-dimensional Broer-Kaup-Kupershmidt (BKK), Kolmogorov-Petrovskii-Piskunov (KPP) equations. Firstly, an algebraic system obtained reducing partial differential (NLPDE) ordinary under tra...

In this short note we discuss a new formula for solving the nonlocal $\overline{\partial}$-problem, and application to Manakov--Zakharov dressing method. We then explicitly apply complex (2+1)D Kadomtsev--Petviashvili equation completely integrable generalization of Kaup--Broer (or Kaup--Boussinesq) system. will also how real (1+1)D solutions are expressed using formalism. It is simple express ...

We use the integrable Kaup-Boussinesq shallow water system, modified by a small viscous term, to model the formation of an undular bore with a steady profile. The description is made in terms of the corresponding integrable Whitham system, also appropriately modified by viscosity. This is derived in Riemann variables using a modified finite-gap integration technique for the Ablowitz-Kaup-Newell...