The modified Kadomtsev-Petviashvili (mKP) equation is shown in this paper to be decomposable into the first two soliton equations of the 2N -coupled Chen-Lee-Liu and Kaup-Newell hierarchies by respectively nonlinearizing two sets of symmetry Lax pairs. In these two cases, the decomposed (1+1)-dimensional nonlinear systems both have a couple of different Lax representations, which means that the...

The " truncation procedure " initiated by Weiss et al. is best understood as a Darboux transformation. If it leads to the Lax pair of the PDE under study, the Bäcklund transformation follows by an elimination, thus proving the integrability. We present the state of the art of this powerful technique. The easy situations were all handled by the WTC one–family truncation and its homographically i...

The purpose of the present study is to propose a scheme to estimate whole-body averaged specific absorption rate (WBA-SAR) in the whole-body resonance and GHz frequency regions. The motivation is that WBA-SARs in the child models in these frequency regions have been reported to approach to the basic restrictions in the international guidelines/standards. In the resonance frequency region, we pr...

In the last two decades the Inverse Spectral Transform (IST) method has been generalized and successfully applied to various (2 + 1)-dimensional nonlinear evolution equations such as Kadomtsev–Petviashvili, Davey–Stewardson, Nizhnik–Veselov–Novikov, Zakharov–Manakov system, Ishimory, two dimensional integrable sine-Gordon and others (see books [1, 2, 3, 4] and references therein). The nonlocal ...

The generation of an undular bore in the vicinity of a wave-breaking point is considered for the integrable Kaup–Boussinesq (KB) shallow water system. In the framework of the Whitham modulation theory, an analytic solution of the Gurevich–Pitaevskii type of problem for a generic “cubic” breaking regime is obtained using a generalized hodograph transform, and a further reduction to a linear Eule...

In this paper we discuss the two-step simulation hypothesis of negation processing proposed by Kaup et al. [3,4] with regard to negating two sorts of predicates: those with clear opposites (“long” vs “short”, “closed” vs “open”) and those without clear opposites (“red”, “triangle”). The hypothesis by Kaup et alia predicts that negation is integrated into sentence meaning on the later stage of s...

Algebro-geometric solutions of the lattice potential modified Kadomtsev-Petviashvili (lpmKP) equation are constructed. A Darboux transformation Kaup--Newell spectral problem is employed to generate a Lax triad for lpmKP equation, as well define commutative integrable symplectic maps which discrete flows eigenfunctions. These share same integrals with finite-dimensional Hamiltonian system associ...