In this paper, the Painlevé integrable property of (1 + 1)-dimensional generalized Broer–Kaup (gBK) equations is first proven. Then, Bäcklund transformations for gBK are derived by using truncation. Based on a special case transformations, linearized into heat conduction equation. Inspired reduced Burgers Starting from linear equation, two forms N-soliton solutions and rational with singularity...

A test of flexibility, so widely used that it deserves to be called the classical measure, is hip flexion. It has featured in a variety of guises as the toe-touch test (Weber and Kraus, 1949; Buxton, 1957; Larson, 1974) the sit and reach test (Wells and Dillon, 1952), the femoral trunk angle (Troup, Hood and Chapman, 1968) and supine leg lift (Tanigawa, 1972). Harris (1969) reports on its high ...

Based on two higher-dimensional extensions of Lie algebras, three kinds of specific Lie algebras are introduced. Upon constructing proper loop algebras, six isospectral matrix spectral problems are presented and they yield nonlinear integrable couplings of the AblowitzKaup-Newell-Segur hierarchy, the Broer-Kaup hierarchy and the Kaup-Newell hierarchy. Especially, the reduced cases of the result...

This paper presents the semi-analytical analysis of fractional-order non-linear coupled system Whitham-Broer-Kaup equations. An iterative process is designed to analyze analytical findings specified partial fractional derivatives scheme utilizing Yang transformation with Adomian technique. The derivative considered in sense Caputo-Fabrizio. Two numerical problems show suggested method. Moreover...

In this paper, Whitham–Broer–Kaup (WBK) equations with time-dependent coefficients are exactly solved through Hirota’s bilinear method. To be specific, the WBK equations are first reduced into a system of variable-coefficient Ablowitz–Kaup– Newell–Segur (AKNS) equations. With the help of the AKNS equations, bilinear forms of the WBK equations are then given. Based on a special case of the bilin...

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...

By means of the Weiss-Tabor-Carnevale truncation method and the general variable separation approach, analytical investigation of the integrable (2+1)dimensional higher order Broer-Kaup system shows, due to the possibility of selecting three arbitrary functions, the existence of interacting coherent excitations such as dromions, solitons, periodic solitons etc... The interaction between some of...

This paper discusses several algorithmic ways of constructing integrable evolution equations based on Lie algebraic structure. We derive, in a pedagogical style, a large class of two component peakon type dual systems from their two component soliton equations counter part. We study the essential aspects of Hamiltonian flows on coadjoint orbits of the centrally extended semidirect product group...