In this letter, He’s Variational iteration method (VIM) is implemented for solving the nonlinear Whitham-Broer-Kaup partial differential equations. This method is based on Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method creates a sequence which tends to the exact solution of the problem. The results are compared with those obtained by t...

This work presents a derivation of the energy density and energy flux of surface waves modeled by the so-called Kaup system, a variant of the Boussinesq system. The derivation is based on reconstruction of the velocity field and the pressure in the fluid column below the free surface, and is an extension of a method recently proposed in [2]. In the present note, it is shown that the total energ...

In this paper, we present new Hamiltonian operators for the integrable couplings of Ablowitz–Kaup–Newell–Segur hierarchy and Kaup–Newell hierarchy. The corresponding Hamiltonians allow nontrivial degeneration. Multi-Hamiltonian structures are investigated. involutive property is proven known with respect to two Poisson brackets defined by operators.

By using gauge transformations, we manage to obtain new solutions of (2 + 1)dimensional Kadomtsev-Petviashvili(KP), Kaup-Kuperschmidt(KK) and SawadaKotera(SK) equations from non-zero seeds. For each of the preceding equations, a Galilean type transformation between these solutions u2 and the previously known solutions u2 generated from zero seed is given. We present several explicit formulas of...

hepcidin is an innate immune element which decreases the iron absorption from diet and iron releasing from macrophage cell. in contrast to the chemical iron chelators, there has been limited effort applied to the specific use of hepcidin as a new drug for decreasing the iron overload. hepcidin is produced in different biological systems. for instance, e-coli is used for human hepcidin expressio...

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...

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and Applied Analysis 3 (2) If 0 < g < g0, we get a solitary wave solution u6 ( x, y, t ) c (√ 2 α − 1 β cosh θ ( x y − ct )) α − 1 ( 1 β − cosh 2θ ( x y − ct )) α ( −1 α β − α − 1 cosh 2θ ( x y − ct )) , 2.4 and two blow-up solutions u7± ( x, y, t ) c ( α ( 2 β ) − 2 − 2 α − 1 cosh θ ( x y − ct ) ± β 3/2 coth θ/2 ( x y − ct )) 2α ( −1 α β − α − 1 cosh θ ( x y − ct )) , 2.5 where β 6 − 6α α2 and...

We have successfully built and operated a source deployment system for the KamLAND detector. This system was used to position radioactive sources throughout the delicate 1-kton liquid scintillator volume, while meeting stringent material cleanliness, material compatibility, and safety requirements. The calibration data obtained with this device were used to fully characterize detector position ...