In this paper, a novel image encryption scheme is presented that leverages a combination of hyperchaotic systems, Singular Value Decomposition (SVD), RC5 operations, permutation techniques, and a custom S-box generated via the XORshift algorithm. Multiple satellite images are merged into a single augmented image prior to encryption by this algorithm, effectively protecting against traffic analysis attacks that could compromise individual encrypted images. Once the augmented image is created, it is split into RGB color channels, and each channel undergoes a four-stage encryption process. The encryption process is initiated by the generation of a chaotic sequence from a six-dimensional (6D) hyperchaotic system. This initial key sequence is then manipulated and transformed into a new key using SVD. The transformed key sequence is utilized to XOR the original image, providing an initial layer of encryption. Subsequently, the image is divided into blocks, and RC5 operations are applied to each block to enhance the security of the encryption process. Following this, a permutation operation is performed on the image using the chaotic sequence generated earlier. Finally, an S-box, created from a random sequence generated by the XORshift algorithm, is applied to the image to further obscure the pixel values. The robustness of the algorithm is validated by numerical tests, demonstrating its effectiveness against both statistical, differential attacks and brute-force attacks, making it extremely difficult for third parties, such as cloud service providers, to identify any relational patterns between the encrypted satellite images. Specific numerical values that demonstrated an enhanced security level include a key space of 27016, entropy exceeding 7.999, and a cross-correlation of ≈ 0. This encryption method not only strengthens the protection of satellite imagery against unauthorized access but also ensures the integrity and confidentiality of the images, which are crucial for applications ranging from national security to environmental monitoring in an increasingly data-driven world.

Our paper studies the optical solitons for the Kundu–Eckhaus (KE) equation with quintic nonlinearity and Raman effect. By applying the improved modified extended tanh-function method, many soliton solutions can be obtained such as bright soliton solutions, dark soliton solutions, and the singular soliton solution. In addition, we can obtain various types of solutions, namely, singular periodic solutions, exponential solutions, rational solutions, Jacobi elliptic solutions and Weierstrass elliptic doubly periodic solutions. Moreover, some selected solutions are illustrated graphically to show the physical nature and the characteristics of the obtained solutions.

In this work, we investigate the optical solitons and other waves through magneto-optic waveguides with Kudryashov’s law of nonlinear refractive index in the presence of chromatic dispersion and Hamiltonian-type perturbation factors using the modified extended mapping approach. Many classifications of solutions are established like bright solitons, dark solitons, singular solitons, singular periodic wave solutions, exponential wave solutions, rational wave, solutions, Weierstrass elliptic doubly periodic solutions, and Jacobi elliptic function solutions. Some of the extracted solutions are described graphically to provide their physical understanding of the acquired solutions.

The nonlinear fractional Klein–Fock–Gordon (KFG) equation represents an advanced theoretical physics and applied mathematical tool that provides a more extraordinary framework for studying fields with complex and non-standard behaviors. Here, we aim to delve into the new wave profiles of this fractional KGF equation. Initially, this system is successfully converted into an ordinary differential equation (ODE) with the help of wave conversion, and the ODE is solved through the unified and unified solver techniques for the first time. In addition, the 3D and 2D plots of these solutions are drawn using a mathematical software package for different parameters with different values. Therefore, some unique waveforms can be found in these solutions. Moreover, stability and multistability analyses are prepared and shown graphically to confirm the converging limitations of appropriate parameters. This work will be practiced more effectively in future research on nonlinear partial differential models.

The multiplicative white noise in the Ito interpretation is included for the first time in the perturbed higher-order modified Gerdjikov–Ivanov (HMGI) equation, that is considered the focus of the current study. In this work, we investigate the suggested model using the improved modified extended tanh-function (IMETF) method with the goal of producing brilliant and unique solitons such as dark and bright solitons, singular and singular periodic solutions, hyperbolic wave solutions, Weierstrass elliptic doubly periodic solutions, rational, exponential function solutions and Jacobi elliptic functions (JEFs). These extracted solutions demonstrate the effectiveness and potency of the used methodology. The used method specifies our research objective, which is related to solitons. These obtained soliton solutions are useful resources for examining a range of phenomena when there is white noise present. We examine how various wave phenomena are affected by noise, with a special emphasis on soliton solutions. Our findings indicate that the phase component for the obtained solitons of the suggested governing model is the primary goal of the white noise. This study is the first to show the optical soliton solutions derived from the perturbed HMGI equation under multiplicative white noise influence. The contribution of our work is the application of this phenomenon to a model equation in a new context that neither has been studied nor discovered before for optical soliton solutions. With the derived findings, our knowledge of wave events in nonlinear optical systems has advanced significantly.