Mohammad Mohammadi

• PhD
• Persian Gulf University

This paper deals with the numerical solutions of a general class of one-dimensional nonlinear partial differential equations (PDEs) arising in different fields of science. The nonlinear equations contain, as special cases, several PDEs such as Burgers equation, nonlinear-Schrödinger equation (NLSE), Korteweg–De Vries (KDV) equation, and KdV–Schrödi...

In this study, based on the φ4 model, a new model (called the Bφ4 model) is introduced in which the potential form for the values of the field whose magnitudes are greater than 1 is multiplied by the positive number B. All features related to a single kink (antikink) solution remain unchanged and are independent of parameter B. However, when a kink...

In this work, the relativistic non-standard Lagrangian densities (k-fields) with massless solutions are generally introduced. Such solutions are not necessarily energetically stable. However, in \(3+1\) dimensions, we introduce a new k-field model that results in a single non-topological massless solitary wave solution. This special solution is ene...

However, for the regime $B >1$, this behavior gradually becomes fuzzing and chaotic as it approaches $B = 3.3$. The case $B = 3.3$ is obtained again as the minimum of the critical speed curve as a function of $B$. For the regime $3.3< B \leq 10$, the chaotic behavior gradually decreases. However, a fractal structure is never observed. Nevertheless,...

The existence of a faster-than-light particle is in direct opposition to Einstein’s relativity and the principle of causality. However, we show that the theory of classical relativistic fields is not inherently inconsistent with the existence of the faster-than-light particle-like soliton solutions in 1+1 dimensions. We introduce two extended KG mo...

We borrow the form of potential of the well-known kink-bearing φ4 system in the range between its two vacua and paste it repeatedly into the other ranges to introduce the periodic φ4 system. The paper is devoted to providing a comparative numerical study of the properties of the two systems. Although the two systems are quite similar for a kink (an...

For a real nonlinear Klein–Gordon Lagrangian density with a special solitary wave solution (SSWS), which is essentially unstable, it is shown how adding a proper additional massless term could guarantee the energetically stability of the SSWS, without changing its dominant dynamical equation and other properties. In other words, it is a stability c...

We borrow the form of potential of the well-known kink-bearing $\varphi^4$ system in the range between its two vacua and paste it repeatedly into the other ranges to introduce the periodic $\varphi^4$ system. The paper is devoted to providing a comparative numerical study of the properties of the two systems. Although the two systems are quite simi...

The paper, classically, presents an extended Klein–Gordon field system in 3 + 1 dimensions with a special Q-ball solution. The Q-ball solution is energetically stable, that is, for any arbitrary small deformation above the background of that, total energy always increases. The general dynamical equations, just for this special Q-ball solution, are...

In this paper we present a new extended complex nonlinear Klein–Gordon Lagrangian density, which bears a single non-topological soliton solution with a specific rest frequency ωs in 1+1 dimensions. There is a proper term in the new Lagrangian density, which behaves like a massless spook that surrounds the single soliton solution and opposes any int...

In this paper, extended Klein-Gordon field systems will be introduced. Theoretically, it will be shown that for a special example of these systems, it is possible to have a single zero rest mass soliton solution, which is forced to move at the speed of light provided it is considered a non-deformed rigid object. This special soliton solution has th...

The paper, classically, presents an extended Klein-Gordon field system in $3+1$ dimensions with a special Q-ball solution. The Q-ball solution is energetically stable, that is, for any arbitrary small deformation above the background of that, total energy always increases. The general dynamical equations, just for this special Q-ball solution, are...

In this work, the relativistic non-standard Lagrangian densities (k-fields) with massless solutions are generally introduced. Such solutions are not necessarily energetically stable. However, in 3+1 dimensions, we introduce a new k-field model that results in a single non-topological massless solitary wave solution. This special solution is energet...

Inspired by the well known sine-Gordon equation, we present a symmetric coupled system of two real scalar fields in 1+1 dimensions. There are three different topological soliton solutions which be labelled according to their topological charges. These solitons can absorb some localized non-dispersive wave packets in collision processes. It will be...

Inspired by the well known sine-Gordon equation, we present a symmetric coupled system of two real scalar fields in $1+1$ dimensions. There are three different topological soliton solutions which be labelled according to their topological charges. These solitons can absorb some localized non-dispersive wave packets in collision processes. It will b...

We intend to introduce classically a special Lagrangian density in such a way that, firstly, it leads to a special non-topological solitary wave solution, secondly, the stability of that is guaranteed properly, and thirdly, its dominant dynamical equations reduce to the standard nonlinear Klein-Gordon equations. For these purposes, we have to consi...

We intend to introduce classically a special Lagrangian density in such a way that, firstly, it leads to a special non-topological solitary wave solution, secondly, the stability of that is guaranteed properly, and thirdly, its dominant dynamical equations reduce to the standard nonlinear Klein–Gordon equations. For these purposes, we have to consi...

For a real nonlinear Klein-Gordon Lagrangian density with a special solitary wave solution (SSWS), which is essentially unstable, it is shown how adding a proper additional massless term could guarantee the energetically stability of the SSWS, without changing its dominant dynamical equation and other properties. In other words, it is a stability c...

In this paper, extended Klein-Gordon (KG) field systems will be introduced. Theoretically, it will be shown that for a special example of them, it is possible to have a single zero rest mass soliton solution which is forced to move at the speed of light provided it is considered as a non-deformed rigid object. This special soliton solution has the...

In this paper, we present soliton-like solutions of the non-linear complex Klein-Gordon systems in 1+1 dimensions. We will use polar representation to introduce three different soliton-like solutions including, complex kinks (anti-kinks), radiative-profiles, and localized wave-packets. Complex kinks (anti-kinks) are topological objects with zero el...

In this paper we present a new extended complex non-linear Klein-Gordon Lagrangian density which bears a single non-topological wave packet soliton solutions with a specific rest frequency $\omega_{s}$ in $1+1$ dimensions. There is a proper term in the new Lagrangian density which behaves like a massless spook that surrounds the single soliton solu...

The paper, classically, presents a special stable non-topological solitary wave packet solution in $3+1$ dimensions for an extended complex non-linear Klein-Gordon (CNKG) field system. The rest energy of this special solution is minimum among other (close) solutions i.e. it is a soliton solution. The equation of motion and other properties for this...

In this paper, we present the complex sine-Gordon system as a nonlinear complex Klein–Gordon equation in $1+1$-dimensional space-time. Soliton-like solutions in the form of kinks (anti-kinks) and radiative profiles are two different soliton-like solutions that will be discussed in detail in this paper. Complex kinks (anti-kinks) are topological obj...

In this paper, we study the nonlinear sin^4(ϕ) system in 1+1 dimensions which exhibits interesting nonlinear properties. We have categorized the system as radiative, since the collision of a kink and an antikink with velocities less than a threshold velocity leads to the complete annihilation of the pair and production of two high-amplitude wave pa...

In this paper, we study the nonlinear sin(4)(phi) system in 1+1 dimensions which exhibits interesting nonlinear properties. We have categorized the system as radiative, since the collision of a kink and an antikink with velocities less than a threshold velocity leads to the complete annihilation of the pair and production of two high-amplitude wave...

After a quick review of the Lane-Emden equation and its properties, a composite of two different polytropes is introduced and some of the consequences are explored. The results are used to build a nonlinear electromagnetism with non-singular, solitonic solutions as charged particles.

A new, one-parameter family of potentials is introduced. This potential leads to a nonlinear field equation with kink solutions. Internal modes of these solutions are calculated. Conditions on the parameter of the model are obtained which lead to the elimination of extra bound states and nearly reflection-less behavior of the solutions. We discuss...

Solitary wave and soliton solutions of nonlinear equations are well known for physicists. A soliton is a solitary wave with some outstanding features which make it reasonable to be studied seriously in nonlinear systems. In fact most of the nonlinear systems which have solitary wave solutions, has no soliton solutions. To realize a solitary wave as...