Evolution Behaviour of Kink Breathers and Lump-M-Solitons (M → ∞) for the (3+1)-Dimensional Hirota-Satsuma-Ito-Like Equation

In this paper, some novel lump solutions and interaction phenomenon between lump and kink M-soliton are investigated. Firstly, we study the evolution and degeneration behaviour of kink breather wave solution with difffferent forms for the (3+1)-dimensional Hirota-Satsuma-Ito-like equation by symbolic computation and Hirota bilinear form. In the process of degeneration of breather waves, some novel lump solutions are derived by the limit method. In addition, M-fifissionable soliton and the interaction phenomenon between lump solutions and kink M-solitons (lump-M-solitons) are investigated, the theorem and corollary about the conditions for the existence of the interaction phenomenon are given and proved further. The lump-M-solitons with difffferent types is studied to illustrate the correctness and availability of the given theorem and corollary, such as lump-cos type, lump-cosh-exponential type, lump cosh-cos-cosh type. Several three-dimensional fifigures are drawn to better depict the nonlinear dynamic behaviours including the oscillation of breather wave, the emergence of lump, the evolution behaviour of fission and fusion of lump-M-solitons and so on.

Y-shaped soliton solutions for the (2+1)-dimensional bidirectional Sawada–Kotera equation

On the basis of the Hirota bilinear method, resonance Y-shaped soliton and its interaction with other localized waves of (2+1)-dimensional bidirectional Sawada–Kotera equation are derived by introducing the constraint conditions. These types of mixed soliton solutions exhibit complex interaction phenomenon between the resonance Y-shaped solitons and line waves, breather waves, and high-order lump waves. The dynamic behaviors of the interaction solutions are analyzed and illustrated.

Interaction Analysis of Simple form Objects with Fluid and Control Optimization

Fluid-rigid body interaction is an age-old phenomenon, but interestingly, a good approximated solution for the phenomenon pertaining to non-stationary body-fluid interaction is still non-existent. The solution is much more complicated due to huge system of simultaneous partial differential equations that are framed from multi-degrees of freedom, all elements in the spatial domain coupled together between all time steps. Additionally, when considering the spatial aspects of solving the system of partial differential equations, there arise a range of complexities from the type of solution technique (finite-differences, finite-volume, finite-element) and also from meshing techniques (moving, structured or unstructured). Even though advanced commercial fluid-structure interaction solvers are available, they are limited to simple objects and require frequent remeshing techniques that are time consuming and computationally expensive. The promotion work specifically focuses solely on rigid body-fluid (air) interaction and does not consider flow reattachment or flow separation phenomenon offering an alternative approach to study the interaction phenomenon and its advantages. The basic idea of the approximated theory in the current work is to have a simplified approach through a straightforward mathematical model without considering the viscous nature of fluid medium (air). Therefore, this is an approximate theory for non-stationary body and fluid interaction phenomenon considering inputs (post-processing results) from stationary rigid body-fluid interaction performed in ANSYS Fluent (2D and 3D) where the steady state RANS equation is solved with the help of turbulence model. The concept discussed in the work will offer an alternative approach for ‘space-time’ programming techniques and also help to solve the engineering tasks of optimization and synthesis for simple form objects without requiring huge computational efforts. A new world of science for autonomous robots (underwater robotic fish with single and dual tail actuator) is explored where in an on-board power pack technique (energy scavenging from surrounding medium) is proposed that purely based on the fluid and rigid body interaction phenomenon is analysed. Experiments on simple form objects were performed in ARMFIELD wind tunnel, available at Riga Technical University, at a constant speed of 10 m/s and validated with the computer program ANSYS Fluent (in 3D). All the latest techniques, advantages and importance related to fluid-structure interaction phenomenon are summarized in the literature review section through various databases available over internet.

Diversity of interaction phenomenon, cross-kink wave, and the bright-dark solitons for the (3 + 1)-dimensional Kadomtsev–Petviashvili–Boussinesq-like equation

The (3 + 1)-dimensional Kadomtsev–Petviashvili–Boussinesq-like equation has certain advantages in solving engineering problems. In this paper, based on the generalized bilinear form, we successfully derived the diversity of exact solutions under certain constraints by using the symbolic computation Maple. These solutions have interaction wave solitons, cross-kink wave solitons, and bright-dark solitons. To ensure the accuracy of these solutions, we made a special selection of the parameters involved and made a three-dimensional graph, density graph, and contour graph to illustrate the dynamics of the solutions. The resulting solutions can be used for the study of certain phenomena in physics.

Rational solutions and their interactions with kink and periodic waves for a nonlinear dynamical phenomenon

Lump (rational) waves and their interactions with kink and periodic waves, periodic cross-lump solutions will be discussed for (2+1)-dimensional Maccari-system in this paper. With the combination of rational, exponential, and trigonometric functions, we will study various lump soliton solutions. We will find out analytical solutions with interaction phenomenon and also describe them in graphical ways.

Resonance Y-shaped soliton and interaction solutions in the (2 + 1)-dimensional B-type Kadomtsev–Petviashvili equation

The ([Formula: see text])-dimensional B-type Kadomtsev–Petviashvili (BKP) equation is utilized to depict weakly dispersive waves propagating in the fluid mechanics. According to [Formula: see text]-soliton solutions, resonance Y-shaped soliton and its interaction with other local wave solutions of the ([Formula: see text])-dimensional BKP equation are derived by introducing the constraint conditions. These types of hybrid soliton solutions exhibit the complex interaction phenomenon among resonance Y-shaped solitons, breather waves, line solitary waves and high-order lump waves. The dynamic behaviors of such interaction solutions are analyzed and illustrated.

Effective Sorption of Europium Ions by Interpolymer System Based on Industrial Ion-Exchanger Resins Amberlite IR120 and AB-17-8

The research is aimed at checking the impact of a remote interaction phenomenon on growth of sorption properties of ion-exchange resins during sorption of europium ions. Industrial ion exchangers Amberlite IR120 and AB-17-8 were selected as objects for the study. Investigation was undertaken using the following physico-chemical methods of analysis: conductometry, pH-metry, colorimetry, Fourier transform infrared (FTIR) spectroscopy, thermogravimetric analysis (TGA), and atomic emission spectroscopy. Remote interaction of the initial ion exchangers in the interpolymer system leads to their transition into highly ionized state due to formation of optimal conformation. Found that high ionization areas of Amberlite IR120 and AB-17-8 are the molar ratios Amberlite IR120:AB-17-8 = 4:2 and 1:5. The remote interaction effect provides significant increase of the following sorption properties: sorption degree, polymer chain binding degree, effective dynamic exchange capacity. A strong increase of the sorption properties (average increase for all time of remote interaction is over 50%) in the interpolymer system Amberlite IR120-AB-17-8 was observed with individual polymer structures of Amberlite IR120 and AB-17-8. The remote interaction phenomenon can be successfully used for effective modification of industrial ion exchangers for sorption of rare-earth metals.

Interaction solutions of a variable-coefficient Kadomtsev–Petviashvili equation with self-consistent sources

Under investigation is a generalized variable-coefficient Kadomtsev–Petviashvili equation with self-consistent sources. Our main job is divided into four parts: (i) lump wave solution, (ii) interaction solutions between lump and solitary wave, (iii) breather wave solution and (iv) interaction solutions between lump and periodic wave. Furthermore, the interaction phenomenon of waves is shown in some 3D- and contour plots.