Table 2 Comparative analysis of analytical solution methods.
Methods | Solution classes | Specific solutions | Methodological advantages |
|---|---|---|---|
Kumar-Malik (KM) | \(\bullet\) Soliton solutions | \(\bullet\) Bright/dark soliton profiles | \(\bullet\) Exact solution capability |
\(\bullet\) Jacobi elliptic functions | \(\bullet\) Singular wave solutions | \(\bullet\) Unified treatment of periodic/localized structures | |
\(\bullet\) Hyperbolic solutions | \(\bullet\) Trigonometric function solutions | ||
\(\bullet\) Periodic wave families | \(\bullet\) Exponential-form solutions | ||
\(\bullet\) Hybrid solution forms | |||
Generalized Arnous (GA) | \(\bullet\) Exponential-function bases | \(\bullet\) Rogue wave phenomena | \(\bullet\) Exceptional solution diversity |
\(\bullet\) Composite wave structures | \(\bullet\) Exponentially decaying solutions | \(\bullet\) Adaptive ansatz formulation | |
\(\bullet\) Algebraic-exponential hybrids | |||
Energy Balance (EB) | \(\bullet\) Periodic solutions | \(\bullet\) Approximate wave solutions | \(\bullet\) Non-perturbative approach |
\(\bullet\) Breather-type excitations | \(\bullet\) Avoids solution linearization |
