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Evolution of Nonlinear Wave Pulses in the sine-Gordon Equation Theory
AbstractThe solution to the Whitham modulation equations for envelopes of one-phase periodic waves evolving according to the sine-Gordon equation is...
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Evolution equation for elastic scattering of hadrons
We turn high energy elastic scattering of hadrons into an initial value problem using an evolution equation based on the Regge Field Theory, which...
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Global Existence and Finite-Time Blow-Up for a Nonlinear Nonlocal Evolution Equation
We study the Cauchy problem for a nonlinear nonlocal evolution equation arising in the study of oceanic flows in equatorial regions. We present a...
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Wave–wave interaction of an extended evolution equation with complete Coriolis parameters
An extended evolution equation is studied by means of Hirota bilinear method in this article, and it is gained from local Cartesian coordinate system...
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Revisitation of “implicit quiescent optical solitons with complex Ginzburg–Landau equation having nonlinear chromatic dispersion": generalized temporal evolution
This paper is a revisitation to the study on the retrieval of quiescent optical solitons to the complex Ginzburg–Landau equation that is considered...
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New solitary wave solutions of generalized fractional Tzitzéica-type evolution equations using Sardar sub-equation method
In this study, Sardar sub-equation method is employed to obtain the solitary wave solutions for generalized fractional Tzitzéica type equations. By...
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Hybridization of a Linear Viscoelastic Constitutive Equation and a Nonlinear Maxwell-Type Viscoelastoplastic Model, and Analysis of Poisson’s Ratio Evolution Scenarios under Creep
AbstractA generalization of a physically nonlinear Maxwell-type viscoelastoplastic constitutive equation with four material functions is formulated,...
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Constitutive equation and microstructure evolution during isothermal compression of an Fe–26.6Mn–9.8Al–1.0C lightweight steel
This study investigates the constitutive equation and microstructure evolution of an experimental Fe–26.6Mn–9.8Al–1.0C lightweight steel at...
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Free Evolution
As we mentioned in the previous chapter, the “free evolution” approach is by far the most commonly used today in Numerical Relativity codes. It...
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The mixed solutions for soliton–breather–lump in the (3+1)-dimensional nonlinear evolution equation
In this paper, a (3+1)-dimensional nonlinear evolution equation is studied. By the methods of the Hirota bilinear method and the long wave limit...
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Quantum master equation for the vacuum decay dynamics
The quantum master equation required to describe the dynamics of gravity-related vacuum decay is still challenging. We aim to study this issue. Our...
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Evolution of Heterogeneous Systems
In this chapter we apply the ideas and methods developed in previous chapters to the dynamics of heterogeneous systems and obtain the celebrated...
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Investigation of travelling wave solutions for the (3 + 1)-dimensional hyperbolic nonlinear Schrödinger equation using Riccati equation and F-expansion techniques
The (3 + 1)-dimensional hyperbolic nonlinear Schrödinger equation (HNLS) is used as a model for different physical phenomena such as the propagation...
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Travelling wave solutions for hierarchy of nonlinear evolution equation description propagation pulse in optical fibers
In this paper, the improved extended modified tanh function method is applied to hierarchy of nonlinear partial evolution equation that model the...
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Relativistic Boltzmann Equation
The special and general relativistic generalizations of the Boltzmann equation are considered as well as the methods to solve this equation—the...
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Multi-collinear splitting kernels for track function evolution
Jets and their substructure play a central role in many analyses at the Large Hadron Collider (LHC). To improve the precision of measurements, as...
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Equation of State of Materials
Equation of state (EOS)—a macroscopic representation of the thermodynamic state of materials under static and shock compression, is amongst the most...
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Evolution of primordial black holes in f(Q) gravity with non-linear equation of state
We study evolution of primordial black holes (PBH) in the f ( Q ) modified gravity for matter accretion from the cosmic fluid surrounding the PBH. For...
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The Wave Equation
In 1925, quantum mechanics was put on solid ground when Erwin Schrödinger discovered the equation that is named after him today. It was then clear...