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Considered in this paper is the Camassa–Holm–Kadomtsev–Petviashvili (CH–KP) equation [22], which can be obtained as a model for the propagation of shallow water waves over a flat bed. It is shown that the existence of periodic peaked solitary-wave solutions to this model equation. In addition, we show that there are a multitude of solitary waves such as smooth, peakons, cuspons, stumpons, and composite like as CH equation.

This paper is concerned with the initial boundary value problem for viscoelastic Kirchhoff-like plate equation with rotational inertia, memory, $p$-Laplacian restoring force, weak damping, strong damping, and nonlinear source terms. We establish the local existence and uniqueness of the solution by linearization and contraction mapping principle. Then we obtain the global existence of solution with subcritical and critical initial energy by applying potential well theory. Then we prove the asymptotic behavior of the global solution with positive initial energy strictly below the depth of potential well. Finally, we conduct a comprehensive study on the finite time blow-up of solution with negative initial energy, null initial energy, and positive initial energy strictly below the depth of potential well and arbitrary positive initial energy, respectively.

In this paper, we consider an asymptotic model for wave propagation in shallow water with the effect of the Coriolis force is derived from the governing equation in two dimensional flows. Motivated by the eariler works (Brandolese in Int Math Res Not 22:5161–5181, 2012; Escauriaza et al. in J Funct Anal 244:504–535, 2007; Himonas et al. in Commun Math Phys 271:511–522, 2007; Himonas and Misiolek in Math Ann 327:575–584, 2003; Kohlmann in Z Angew Math Mech 94:264–272, 2014), we demonstrate the persistence results for the solution in weighted $$L^p$$ spaces for a large classs of moderate weights. We also discuss the spatial asymptotic profiles of solutions to this model equation. Finally, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time.

In this paper, we study the existence of periodic peaked solitary waves to a generalized μ-Camassa–Holm–Novikov equation with nonlocal cubic and quadratic nonlinearities. The equation is a μ-versio...

In this paper, we study the existence of peaked traveling wave solution of the generalized μ-Novikov equation with nonlocal cubic and quadratic nonlinearities. The equation is a μ-version of a linear combination of the Novikov equation and Camassa-Hom equation. It is found that the equation admits single peaked traveling wave solutions.

In this paper, we consider the dissipative Degasperis-Procesi equation with arbitrary dispersion coefficient and compactly supported initial data. We establish the simple condition on the initial data which lead to guarantee that the solution exists globally. We also investigate the propagation speed for the equation under the initial data is compactly supported.

In the present study an asymptotic model for wave propagation in shallow water with the effect of the Coriolis force is derived from the governing equation in two dimensional flows. The transport equation theory is then applied to investigate the local well-posedness and wave breaking phenomena for this model. The nonexistence of the Camassa-Holm-type peaked solution and classification of various traveling-wave solutions to the new system are also established. Moreover it is shown that all the symmetric waves to this model are traveling waves.

We present a general and effective method, known as the Fokas method, to solve an arbitrary discrete linear evolution equation posed in a finite lattice. The method is based on the simultaneous ana...

Considered herein is the periodic rotation-two-component Camassa–Holm system, which can be derived from the f-plane governing equations for the geophysical water waves with a constant underlying current. The nonlocal nonlinearities on blow-up criteria and wave-breaking phenomena are established. Finally, a sufficient condition for global solutions is obtained by using a method of the Lyapunov function.

The existence of global weak solutions is established to the magnetohydrodynamics (MHD) equations with Hall and ion-slip effects in a bounded domain, which coincide with the Hall-MHD equations with and without ion-slip effect for the complementary choices of the parameter $$\gamma =1$$ and $$\gamma =0$$, respectively. It is also shown that a similar result holds in the whole space. Moreover, the local existence of a unique strong solution and the global well-posedness for small initial data are obtained to the Hall-MHD equations with and without ion-slip effect in both a cubic bounded domain with a flat boundary condition and the whole space. Furthermore, the vanishing viscosity limit to inviscid MHD equations is studied without the ion-slip effect ($$\gamma =0$$) in the cubic bounded domain with the flat boundary condition and with the ion-slip effect ($$\gamma =1$$) in the whole space, respectively.

Recently, Zhu et al. (2020) proposed a kind of rotation-Camassa–Holm equation. In this paper, we study the question of nonexistence of periodic peaked traveling wave solution for rotation-Camassa–Holm equation. Indeed, rotation-Camassa–Holm equation has no nontrivial periodic Camassa–Holm peaked solution unlike Camassa–Holm equation, modified Camassa–Holm equation, Novikov equation.

This paper is devoted to studying the dynamical stability of periodic peaked solitary waves for the generalized modified Camassa-Holm equation. The equation is a generalization of the modified Camassa-Holm equation and it possesses the Hamiltonian structure shared by the modified Camassa-Holm equation. The equation admits the periodic peakons. It is shown that the periodic peakons are dynamically stable under small perturbations in the energy space.

The Burgers-αβ equation, which was first introduced by Holm and Staley [4], is considered in the special case where ν = 0 ${\nu=0}$ and b = 3 ${b=3}$ . Traveling wave solutions are classified to the Burgers-αβ equation containing four parameters b , α , ν ${b,\alpha,\nu}$ , and β, which is a nonintegrable nonlinear partial differential equation that coincides with the usual Burgers equation and viscous b-family of peakon equation, respectively, for two specific choices of the parameter β = 0 ${\beta=0}$ and β = 1 ${\beta=1}$ . Under the decay condition, it is shown that there are smooth, peaked and cusped traveling wave solutions of the Burgers-αβ equation with ν = 0 ${\nu=0}$ and b = 3 ${b=3}$ depending on the parameter β. Moreover, all traveling wave solutions without the decay condition are parametrized by the integration constant k 1 ∈ ℝ ${k_{1}\in\mathbb{R}}$ . In an appropriate limit β = 1 ${\beta=1}$ , the previously known traveling wave solutions of the Degasperis–Procesi equation are recovered.

We establish global well-posedness to the generalized weakly dissipative periodic two-component Camassa–Holm system in some special case.

The existence of solitary wave solutions of the generalized two-component Hunter–Saxton system is determined. It is also shown that there are peaked and cusped solitary waves with singularities among those smooth solitary wave solutions.

The gas electron multiplier (GEM) chamber fabricated in this experiment had a double GEM structure, and Ar and CO2 gases were used as the counting and the quencher gases, respectively, with a mixing ratio of Ar : CO2 = 80 : 20. A homemade readout board was used to read the electric signals from the GEM detector. The analog-to-digital converter (ADC) was synchronized with the trigger signal, and the converted digital values were fed to a personal computer (PC) by the data acquisition (DAQ) program. The whole detector system was tested with an Fe-55 radiation source (5.9 keV), and we calculated the mass attenuation coecients for a Cu and an Ar/CO 2 gas mixture under 5.9 keV X-ray irradiation. From the results, we found that the Cu film (cathode) played an important role in the signal generation.