5. Discussion and concluding remarks
As mentioned earlier in the literature section that some researchers
have reported bright, dark, singular soliton solutions to the KMN
equation through diverse methods [19, 20, 33–39]. Consequently, the
researchers picked up only the bright, dark, singular soliton solutions
to an integer order KMN equation without considering obliqueness.
However, in this article, we have explored some new types of bright,
dark, U-shaped periodic, and singular shaped soliton solutions with
different amplitudes to an integer and fractional KMN equation
considering wave obliqueness via the gKM and NAEM. The employed methods
also have extracted some new oblique wave solitons to the studied
equation. It has been demonstrated that the wave profile is changed with
the changing of obliqueness and fractionality. The 3D graphical
illustrations and 2D cross sectional graphics for different values of
various parameters are represented to understand the effects of the
changing values of the parameters over the solutions. In comparison with
the attained solutions [19, 20, 33–39], to the best of authors’
knowledge, the generated bright, dark, U-shaped periodic, and singular
soliton wave solutions are new in conformable derivative and obliqueness
senses, which are not reported in previously published articles. It is
remarkable to perceive that most of the investigated solutions in this
article have diverse structures over the solutions available in the
literature in the wave propagation obliquely and the executed methods
are completely new for the studied equation. Therefore, the acquired
optical solutions may illuminate the researchers for
further studies to explain
pragmatic phenomena of the wave approaching obliqueness in the field of
fiber optics and optical communications. This work provides evidence
that the gKM and NAEM are suitable for acquiring new optical soliton
features in any physical system with or without fractional and
obliqueness conditions.