Overtaking interactions of nonlinear ultra-low frequency multi-shock structures in non-relativistic and ultra-relativistic degenerate plasmas

Figures & data

Figure 1. The overtaking collision profiles between (a) two single-E and (b) two single-ULF shock waves for ultra-relativistic case ${\gamma }_e={\gamma }_{\ell }=4/3$, (c) two single-E and (d) two single-ULF shock waves for non-relativistic case ${\gamma }_e={\gamma }_{\ell }=5/3$ for $\alpha =0.66,$ $\eta$ = 0.01, $k_1=0.8$, and$k_2=1.$

Figure 2. The overtaking collision profiles between (a) three single-E and (b) three single-ULF shock waves for ultra-relativistic case ${\gamma }_e={\gamma }_{\ell }=4/3$, (c) three single-E and (d) three single-ULF shock waves for non-relativistic case ${\gamma }_e={\gamma }_{\ell }=5/3$ for $\alpha =0.66,$ $\eta$ = 0.01, $k_1=0.8$, $k_2=1$ and $k_3=\mathrm{1.2.}$

Figure 3. The nonlinear coefficient A (a) for ultra-relativistic case ${\gamma }_e={\gamma }_{\ell }=4/3$ and (b) for non-relativistic case ${\gamma }_e={\gamma }_{\ell }=5/3$.

Figure 4. The overtaking collision profile between (a) two single-ULF shock waves for ultra-relativistic case ${\gamma }_e={\gamma }_{\ell }=4/3$ and (b) two single-ULF shock waves for non-relativistic case ${\gamma }_e={\gamma }_{\ell }=5/3$ for different values of $\alpha$ at $\eta$ = 0.01, $k_1=0.8$ and $k_2=1$.

Figure 5. The overtaking collision profile between (a) three single-ULF shock waves for ultra-relativistic case ${\gamma }_e={\gamma }_{\ell }=4/3$ and (b) three single-ULF shock waves for non-relativistic case ${\gamma }_e={\gamma }_{\ell }=5/3$ for different values of $\eta$ at $\alpha =0.66$, $k_1=0.8$, $k_2=1$ and $k_3=\mathrm{1.2.}$