Large Amplitude Electrostatic (Un)modulated Excitations in Anisotropic Magnetoplasmas: Solitons and Freak Waves

Abstract

The arbitrary amplitude ion-acoustic (IA) (un)modulated electrostatic structures including unmodulated solitary waves (SWs) and freak waves (FWs) in a magnetized and collisionless electron-ion plasma with pressure anisotropy are investigated. The present investigation is divided into two main objectives: for the first one, an energy integral equation is derived using the Sagdeev approach for studying the characteristics of large amplitude unmodulated SWs. The Sagdeev potential is analyzed numerically to confine the existence regions of large amplitude SWs and for determining the polarity of the SWs. The numerical analysis of the present model shows that only positive potential nonlinear SWs can exist. With respect to the second objective, the FWs are studied by analyzing the two-dimensional-nonlinear Schrodinger equation (2D-NLSE). The requirements for the presence of FWs are discussed based on the physical factors of the present model. The impacts of physical plasma parameters on the characteristic properties of both unmodulated SWs and FWs are examined. The obtained results are useful in understanding the mystery of many phenomena in astrophysical and space plasmas.

Appendix

The coefficients of the NLSE (38)

$$\begin{aligned} P=&-\frac{\left( -v_{g}k+\omega \right) ^{2}+k^{3}\left[ v_{g}\left( v_{g}k+2\omega \right) -3p_{1}k\right] }{2\omega k^{2}\left( k^{2}+1\right) },\\ Q=&\ \frac{\left( \frac{1-\kappa ^{2}}{2}+g_{3}+g_{6}\right) \left( \omega ^{2}-p_{1}k^{2}\right) }{2\omega \left( k^{2}+1\right) }\\&-\left. \frac{1}{2\omega }\left[ \left( g_{1}+g_{4}\right) \left( \omega ^{2}+p_{1}k^{2}\right) +2k\omega \left( g_{2}+g_{5}\right) \right] \right. ,\\ R=&-\frac{p_{1}k^{2}}{2\omega \left( k^{2}+1\right) }+\frac{\omega \left[ \omega ^{2}-1-\Omega ^{2}-\left( k^{2}+1\right) p_{2}\right] }{2\left( k^{2}+1\right) \left( \omega ^{2}-\Omega ^{2}\right) }. \end{aligned}$$

with

$$\begin{aligned} g_{1}&=\left( 4k^{2}+1\right) g_{3}+\frac{1}{2},\\ g_{2}&=\frac{\omega }{k}g_{1}-\frac{\omega }{k}\left( k^{2}+1\right) ^{2},\\ g_{3}&=\frac{\omega ^{2}-p_{1}k^{2}-\left( k^{2}+1\right) ^{2}\left( 3\omega ^{2}+p_{1}k^{2}\right) }{2\left[ k^{2}-4k^{2}\omega ^{2}-\omega ^{2}+p_{1}k^{2}\left( 4k^{2}+1\right) \right] },\\ g_{4}&=g_{6}+1,\text { }g_{5}=-2\frac{\omega }{k}\left( k^{2}+1\right) ^{2}+v_{g}g_{4},\\ g_{6}&=\frac{k^{2}v_{g}^{2}-2\left( k^{2}+1\right) ^{2}\left( \omega ^{2}+p_{1}k^{2}+kv_{g}\omega \right) }{k^{2}\left( 1-v_{g}^{2}\right) },\\ \omega ^{2}&=p_{1}k^{2}+\frac{k^{2}}{k^{2}+1},\text { }v_{g}=k/\omega \left( p_{1}+1/\left( k^{2}+1\right) ^{2}\right) . \end{aligned}$$