The lump soliton solutions of a (2 + 1)-dimensional asymmetrical Nizhnik–Novikov–Veselov equation are obtained by making use of its bilinear form. We discuss the conditions to guarantee the analyticity, positiveness and localization of lump solutions. The solutions of interaction between a lump and a stripe are presented. It is proved that the interaction between the two solitary waves is non-elastic. The three-wave method is employed to investigate the periodic lump solutions. Figures are presented to illustrate the dynamical features of these solutions.

In this paper, the Lie symmetry analysis method is employed to investigate the Lie point symmetries and the one-parameter transformation groups of a (2 + 1)-dimensional Boiti-Leon-Pempinelli system. By using Ibragimov’s method, the optimal system of one-dimensional subalgebras of this system is constructed. Truncated Painlevé analysis is used for deriving the Bäcklund transformation. The method of constructing lump-type solutions of integrable equations by means of Bäcklund transformation is first presented. Meanwhile, the lump-type solutions of the (2 + 1)-dimensional Boiti-Leon-Pempinelli system are obtained. The lump-type wave is one kind of rogue wave. The fusion-type N-solitary wave solutions are also constructed. In addition, this system is integrable in terms of the consistent Riccati expansion method.

No abstract

No abstract

Full-waveform inversion and reverse time migration rely on an efficient forward-modeling approach. Current 3D large-scale frequency-domain implementations of these techniques mostly extract the desired frequency component from the time-domain wavefields through discrete Fourier transform. However, instead of conducting the time-marching steps for each seismic source, in which the time step is limited by the stability condition, performing the wave modeling directly in the frequency domain using an iterative linear solver may reduce the entire computational complexity. For 2D and 3D frequency-domain elastic wave modeling, a parallel iterative solver based on a conjugate gradient acceleration of the symmetric Kaczmarz row-projection method, named the conjugate-gradient-accelerated component-averaged row projections (CARP-CG) method, shows interesting convergence properties. The parallelization is realized through row-block division and component averaging operations. Convergence is achieved systematically even when different physical factors such as the space-dependent Poisson's ratio, free-surface condition, and seismic attenuation are incorporated in the wave modeling. We determined that the scalability of CARP-CG was satisfactory, especially for large-scale applications, using up to several hundred computational cores. We found a potential improvement in computational complexity compared to timedomain modeling through numerical experiments. Finally, we achieved a convergence at 5 Hz in a 3D heterogeneous model, involving fast-slow-fast layers resembling waveguide geometries, with up to several hundred million unknowns, in fewer than 10 h on fewer than 200 cores. All of these results make CARP-CG a potential candidate of the forward modeling engine for seismic imaging on challenging models.