Multi and breather wave soliton solutions and the linear superposition principle for generalized Hietarinta equation

In this paper, we study the generalized ([Formula: see text])-dimensional Hietarinta equation which is investigated by utilizing Hirota’s bilinear method. Also, the bilinear form is obtained, and the N-soliton solutions are constructed. In addition, multi-wave and breather wave solutions of the addressed equation with specific coefficients are presented. Finally, under certain conditions, the asymptotic behavior of solutions is analyzed in both methods. Moreover, we employ the linear superposition principle to determine [Formula: see text]-soliton wave solutions for the generalized ([Formula: see text])-dimensional Hietarinta equation.

Construction Method of Enterprise-level Database Operational Measurement Platform Based on Bidirectional Coupling Algorithm

When identifying the enterprise database data information, the enterprise database operational dimension measurement platform based on the bilinear method will produce ringing or overshoot effect, the database data monitoring effect is poor as well as the accuracy of operation measurement. To solve this problem, this paper proposes a method to build an enterprise level database operation and maintenance measurement platform based on bidirectional coupling algorithm. Build enterprise database operation measurement platform. The enterprise database monitoring platform is connected with the monitoring database by remote database chain. The Oracle database job scheduling method is used to obtain the monitoring index information in the monitored database, and the database memory performance is comprehensively evaluated by MPI (Memory Perform Index). The platform uses semantic capture layer and related analysis layer to distinguish user behavior, analyze user experience satisfaction, and realize the operation measurement of enterprise level database. The experimental results show that the operational measurement platform built by this method has high throughput, low memory occupancy rate, high measurement accuracy and good user experience.

Bäcklund Transformation and Exact Solutions to a Generalized (3 + 1)-Dimensional Nonlinear Evolution Equation

In this article, a generalized (3 + 1)-dimensional nonlinear evolution equation (NLEE), which can be obtained by a multivariate polynomial, is investigated. Based on the Hirota bilinear method, the N-soliton solution and bilinear Bäcklund transformation (BBT) with explicit formulas are successfully constructed. By using BBT, two traveling wave solutions and a mixed solution of the generalized (3 + 1)-dimensional NLEE are obtained. Furthermore, the lump and the interaction solutions for the equation are constructed. Finally, the dynamic properties of the lump and the interaction solutions are described graphically.

Multiple breathers and high-order rational solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

This paper is devoted to obtaining the multi-soliton solutions, high-order breather solutions and high-order rational solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation by applying the Hirota bilinear method and the long-wave limit approach. Moreover, the interaction solutions are constructed by choosing appropriate value of parameters, which consist of four waves for lumps, breathers, rouges and solitons. Some dynamical characteristics for the obtained exact solutions are illustrated using figures.

Soliton, Breather-Like and Dark-Soliton-Breather-Like Solutions for the Coupled Long-Wave-Short-Wave System

In this paper, we will obtain the exact $N$-soliton solution of the coupled long-wave-short-wave system via the developed Hirota bilinear method. Through manipulating the relevant parameters, we will construct different types of solutions which include breather-like solutions and dark-soliton-breather-like solutions. Moreover, we will demonstrate that the interactions of two-soliton and two-breather-like solutions are all elastic through asymptotic analysis method. Finally, we will display the interactions through illustrations.PACS 05.45.Yv; 02.30.Ik; 42.81.Dp

Exact solutions of the (3+1)-dimensional generalized Boiti–Leon–Manna–Pempinelli equation

In this paper, we study exact solutions of the (3[Formula: see text]+[Formula: see text]1)-dimensional Boiti–Leon–Manna–Pempinelli equation. We employ the Hirota bilinear method to obtain the multi-solitary wave solutions, soliton resonant solutions, periodic solutions and interactional solutions and periodic resonant solutions. The corresponding asymptotic features and images are also clearly given.

Resonance Y-shape Solitons and Mixed Solutions for a (2+1)-dimensional Generalized Caudrey-Dodd-Gibbon-Kotera-Sawada Equation in Fluid Mechanics

Under the well-known bilinear method of Hirota, the specific expression for N-soliton solutions of (2+1)-dimensional generalized Caudrey-Dodd-Gibbon-Kotera-Sawada(gCDGKS) equation in fluid mechanics is given. By defining a noval restrictive condition on N-soliton solutions, resonant Y-type and X-type soliton solutions are generated. Under the previous new constraints, combined with the velocity resonance method and module resonant method, the mixed solutions of resonant Y-type solitons and line waves, breather solutions are found. Finally, with the support of long wave limit method, the interaction between resonant Ytype solitons and higher-order lumps is shown, and the motion trajectory equation before and after the interaction between lumps and resonant Y-type solitons is derived.

Lump-periodic, some interaction phenomena and breather wave solutions to the (2+1)-rth dispersionless Dym equation

In this study, we successfully apply Hirota’s bilinear method (HBM) to retrieve the different wave structures of the general [Formula: see text]th dispersionless Dym equation by considering the test function approaches. The studied model is used to describe the dynamics of deep water waves. We formally retrieve some novel lump periodic, some other new interaction, and breather wave solutions. Moreover, the physical behavior of the reported results is sketched through several three-dimensional, two-dimensional and contour profiles with the assistance of suitable parameters. The acquired results are valuable in grasping the elementary scenarios of nonlinear fluid dynamics as well as the dynamics of engineering sciences in the related nonlinear higher-dimensional wave fields. The gained results are checked and found correct by putting them into the governing equation with the aid of Mathematica. Thus, our strategies through the fortress of representative calculations give a functioning and intense mathematical execution for tackling complicated nonlinear wave issues.

The Soliton Solutions and Long-Time Asymptotic Analysis for an Integrable Variable Coefficient Nonlocal Nonlinear Schrödinger Equation

An integrable variable coefficient nonlocal nonlinear Schrödinger equation (NNLS) is studied; by employing the Hirota’s bilinear method, the bilinear form is obtained, and the N -soliton solutions are constructed. In addition, some singular solutions and period solutions of the addressed equation with specific coefficients are shown. Finally, under certain conditions, the asymptotic behavior of the two-soliton solution is analyzed to prove that the collision of the two-soliton is elastic.

Interaction among a lump, periodic waves, and kink solutions to the KP-BBM equation

The Hirota bilinear method is prepared for searching the diverse soliton solutions to the (2+1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony (KP-BBM) equation. Also, the Hirota bilinear method is used to find the lump and interaction with two stripe soliton solutions. Interaction among lumps, periodic waves, and one-kink soliton solutions are investigated. Also, the solitary wave, periodic wave, and cross-kink wave solutions are examined for the KP-BBM equation. The graphs for various parameters are plotted to contain a 3D plot, contour plot, density plot, and 2D plot. We construct the exact lump and interaction among other types of solutions, by solving the underdetermined nonlinear system of algebraic equations with the associated parameters. Finally, analysis and graphical simulation are presented to show the dynamical characteristics of our solutions, and the interaction behaviors are revealed. The existing conditions are employed to discuss the available got solutions.